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Simplifying 3(x + 5) + -2 = 2(2x + 5) * x Reorder the terms: 3(5 + x) + -2 = 2(2x + 5) * x (5 * 3 + x * 3) + -2 = 2(2x + 5) * x (15 + 3x) + -2 = 2(2x + 5) * x Reorder the terms: 15 + -2 + 3x = 2(2x + 5) * x Combine like terms: 15 + -2 = 13 13 + 3x = 2(2x + 5) * x Reorder the terms: 13 + 3x = 2(5 + 2x) * x Reorder the terms for easier multiplication: 13 + 3x = 2x(5 + 2x) 13 + 3x = (5 * 2x + 2x * 2x) 13 + 3x = (10x + 4x2) Solving 13 + 3x = 10x + 4x2 Solving for variable 'x'. Combine like terms: 3x + -10x = -7x 13 + -7x + -4x2 = 10x + 4x2 + -10x + -4x2 Reorder the terms: 13 + -7x + -4x2 = 10x + -10x + 4x2 + -4x2 Combine like terms: 10x + -10x = 0 13 + -7x + -4x2 = 0 + 4x2 + -4x2 13 + -7x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 13 + -7x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -3.25 + 1.75x + x2 = 0 Move the constant term to the right: Add '3.25' to each side of the equation. -3.25 + 1.75x + 3.25 + x2 = 0 + 3.25 Reorder the terms: -3.25 + 3.25 + 1.75x + x2 = 0 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + 1.75x + x2 = 0 + 3.25 1.75x + x2 = 0 + 3.25 Combine like terms: 0 + 3.25 = 3.25 1.75x + x2 = 3.25 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = 3.25 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 3.25 + 0.765625 Combine like terms: 3.25 + 0.765625 = 4.015625 0.765625 + 1.75x + x2 = 4.015625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 4.015625 Calculate the square root of the right side: 2.003902443 Break this problem into two subproblems by setting (x + 0.875) equal to 2.003902443 and -2.003902443.Subproblem 1
x + 0.875 = 2.003902443 Simplifying x + 0.875 = 2.003902443 Reorder the terms: 0.875 + x = 2.003902443 Solving 0.875 + x = 2.003902443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = 2.003902443 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 2.003902443 + -0.875 x = 2.003902443 + -0.875 Combine like terms: 2.003902443 + -0.875 = 1.128902443 x = 1.128902443 Simplifying x = 1.128902443Subproblem 2
x + 0.875 = -2.003902443 Simplifying x + 0.875 = -2.003902443 Reorder the terms: 0.875 + x = -2.003902443 Solving 0.875 + x = -2.003902443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = -2.003902443 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -2.003902443 + -0.875 x = -2.003902443 + -0.875 Combine like terms: -2.003902443 + -0.875 = -2.878902443 x = -2.878902443 Simplifying x = -2.878902443Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.128902443, -2.878902443}
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