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Simplifying 40 + -4(x + 3) = (5x)(x + 1) Reorder the terms: 40 + -4(3 + x) = (5x)(x + 1) 40 + (3 * -4 + x * -4) = (5x)(x + 1) 40 + (-12 + -4x) = (5x)(x + 1) Combine like terms: 40 + -12 = 28 28 + -4x = (5x)(x + 1) Remove parenthesis around (5x) 28 + -4x = 5x(x + 1) Reorder the terms: 28 + -4x = 5x(1 + x) 28 + -4x = (1 * 5x + x * 5x) 28 + -4x = (5x + 5x2) Solving 28 + -4x = 5x + 5x2 Solving for variable 'x'. Combine like terms: -4x + -5x = -9x 28 + -9x + -5x2 = 5x + 5x2 + -5x + -5x2 Reorder the terms: 28 + -9x + -5x2 = 5x + -5x + 5x2 + -5x2 Combine like terms: 5x + -5x = 0 28 + -9x + -5x2 = 0 + 5x2 + -5x2 28 + -9x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 28 + -9x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -5.6 + 1.8x + x2 = 0 Move the constant term to the right: Add '5.6' to each side of the equation. -5.6 + 1.8x + 5.6 + x2 = 0 + 5.6 Reorder the terms: -5.6 + 5.6 + 1.8x + x2 = 0 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + 1.8x + x2 = 0 + 5.6 1.8x + x2 = 0 + 5.6 Combine like terms: 0 + 5.6 = 5.6 1.8x + x2 = 5.6 The x term is 1.8x. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8x + 0.81 + x2 = 5.6 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = 5.6 + 0.81 Combine like terms: 5.6 + 0.81 = 6.41 0.81 + 1.8x + x2 = 6.41 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = 6.41 Calculate the square root of the right side: 2.53179778 Break this problem into two subproblems by setting (x + 0.9) equal to 2.53179778 and -2.53179778.Subproblem 1
x + 0.9 = 2.53179778 Simplifying x + 0.9 = 2.53179778 Reorder the terms: 0.9 + x = 2.53179778 Solving 0.9 + x = 2.53179778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = 2.53179778 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 2.53179778 + -0.9 x = 2.53179778 + -0.9 Combine like terms: 2.53179778 + -0.9 = 1.63179778 x = 1.63179778 Simplifying x = 1.63179778Subproblem 2
x + 0.9 = -2.53179778 Simplifying x + 0.9 = -2.53179778 Reorder the terms: 0.9 + x = -2.53179778 Solving 0.9 + x = -2.53179778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = -2.53179778 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -2.53179778 + -0.9 x = -2.53179778 + -0.9 Combine like terms: -2.53179778 + -0.9 = -3.43179778 x = -3.43179778 Simplifying x = -3.43179778Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.63179778, -3.43179778}
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