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Simplifying 7(x + 1) * 3 + -3(x + 5) * 2 + -4(x + 1)(x + -2) + -2 = 0 Reorder the terms: 7(1 + x) * 3 + -3(x + 5) * 2 + -4(x + 1)(x + -2) + -2 = 0 Reorder the terms for easier multiplication: 7 * 3(1 + x) + -3(x + 5) * 2 + -4(x + 1)(x + -2) + -2 = 0 Multiply 7 * 3 21(1 + x) + -3(x + 5) * 2 + -4(x + 1)(x + -2) + -2 = 0 (1 * 21 + x * 21) + -3(x + 5) * 2 + -4(x + 1)(x + -2) + -2 = 0 (21 + 21x) + -3(x + 5) * 2 + -4(x + 1)(x + -2) + -2 = 0 Reorder the terms: 21 + 21x + -3(5 + x) * 2 + -4(x + 1)(x + -2) + -2 = 0 Reorder the terms for easier multiplication: 21 + 21x + -3 * 2(5 + x) + -4(x + 1)(x + -2) + -2 = 0 Multiply -3 * 2 21 + 21x + -6(5 + x) + -4(x + 1)(x + -2) + -2 = 0 21 + 21x + (5 * -6 + x * -6) + -4(x + 1)(x + -2) + -2 = 0 21 + 21x + (-30 + -6x) + -4(x + 1)(x + -2) + -2 = 0 Reorder the terms: 21 + 21x + -30 + -6x + -4(1 + x)(x + -2) + -2 = 0 Reorder the terms: 21 + 21x + -30 + -6x + -4(1 + x)(-2 + x) + -2 = 0 Multiply (1 + x) * (-2 + x) 21 + 21x + -30 + -6x + -4(1(-2 + x) + x(-2 + x)) + -2 = 0 21 + 21x + -30 + -6x + -4((-2 * 1 + x * 1) + x(-2 + x)) + -2 = 0 21 + 21x + -30 + -6x + -4((-2 + 1x) + x(-2 + x)) + -2 = 0 21 + 21x + -30 + -6x + -4(-2 + 1x + (-2 * x + x * x)) + -2 = 0 21 + 21x + -30 + -6x + -4(-2 + 1x + (-2x + x2)) + -2 = 0 Combine like terms: 1x + -2x = -1x 21 + 21x + -30 + -6x + -4(-2 + -1x + x2) + -2 = 0 21 + 21x + -30 + -6x + (-2 * -4 + -1x * -4 + x2 * -4) + -2 = 0 21 + 21x + -30 + -6x + (8 + 4x + -4x2) + -2 = 0 Reorder the terms: 21 + -30 + 8 + -2 + 21x + -6x + 4x + -4x2 = 0 Combine like terms: 21 + -30 = -9 -9 + 8 + -2 + 21x + -6x + 4x + -4x2 = 0 Combine like terms: -9 + 8 = -1 -1 + -2 + 21x + -6x + 4x + -4x2 = 0 Combine like terms: -1 + -2 = -3 -3 + 21x + -6x + 4x + -4x2 = 0 Combine like terms: 21x + -6x = 15x -3 + 15x + 4x + -4x2 = 0 Combine like terms: 15x + 4x = 19x -3 + 19x + -4x2 = 0 Solving -3 + 19x + -4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 0.75 + -4.75x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -4.75x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -4.75x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -4.75x + x2 = 0 + -0.75 -4.75x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -4.75x + x2 = -0.75 The x term is -4.75x. Take half its coefficient (-2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. -4.75x + 5.640625 + x2 = -0.75 + 5.640625 Reorder the terms: 5.640625 + -4.75x + x2 = -0.75 + 5.640625 Combine like terms: -0.75 + 5.640625 = 4.890625 5.640625 + -4.75x + x2 = 4.890625 Factor a perfect square on the left side: (x + -2.375)(x + -2.375) = 4.890625 Calculate the square root of the right side: 2.211475752 Break this problem into two subproblems by setting (x + -2.375) equal to 2.211475752 and -2.211475752.Subproblem 1
x + -2.375 = 2.211475752 Simplifying x + -2.375 = 2.211475752 Reorder the terms: -2.375 + x = 2.211475752 Solving -2.375 + x = 2.211475752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = 2.211475752 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = 2.211475752 + 2.375 x = 2.211475752 + 2.375 Combine like terms: 2.211475752 + 2.375 = 4.586475752 x = 4.586475752 Simplifying x = 4.586475752Subproblem 2
x + -2.375 = -2.211475752 Simplifying x + -2.375 = -2.211475752 Reorder the terms: -2.375 + x = -2.211475752 Solving -2.375 + x = -2.211475752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = -2.211475752 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = -2.211475752 + 2.375 x = -2.211475752 + 2.375 Combine like terms: -2.211475752 + 2.375 = 0.163524248 x = 0.163524248 Simplifying x = 0.163524248Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.586475752, 0.163524248}
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