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Simplifying 16x2 + 18x + -18 = 702 Reorder the terms: -18 + 18x + 16x2 = 702 Solving -18 + 18x + 16x2 = 702 Solving for variable 'x'. Reorder the terms: -18 + -702 + 18x + 16x2 = 702 + -702 Combine like terms: -18 + -702 = -720 -720 + 18x + 16x2 = 702 + -702 Combine like terms: 702 + -702 = 0 -720 + 18x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-360 + 9x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-360 + 9x + 8x2)' equal to zero and attempt to solve: Simplifying -360 + 9x + 8x2 = 0 Solving -360 + 9x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -45 + 1.125x + x2 = 0 Move the constant term to the right: Add '45' to each side of the equation. -45 + 1.125x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + 1.125x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 1.125x + x2 = 0 + 45 1.125x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 1.125x + x2 = 45 The x term is 1.125x. Take half its coefficient (0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. 1.125x + 0.31640625 + x2 = 45 + 0.31640625 Reorder the terms: 0.31640625 + 1.125x + x2 = 45 + 0.31640625 Combine like terms: 45 + 0.31640625 = 45.31640625 0.31640625 + 1.125x + x2 = 45.31640625 Factor a perfect square on the left side: (x + 0.5625)(x + 0.5625) = 45.31640625 Calculate the square root of the right side: 6.731746152 Break this problem into two subproblems by setting (x + 0.5625) equal to 6.731746152 and -6.731746152.Subproblem 1
x + 0.5625 = 6.731746152 Simplifying x + 0.5625 = 6.731746152 Reorder the terms: 0.5625 + x = 6.731746152 Solving 0.5625 + x = 6.731746152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + x = 6.731746152 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = 6.731746152 + -0.5625 x = 6.731746152 + -0.5625 Combine like terms: 6.731746152 + -0.5625 = 6.169246152 x = 6.169246152 Simplifying x = 6.169246152Subproblem 2
x + 0.5625 = -6.731746152 Simplifying x + 0.5625 = -6.731746152 Reorder the terms: 0.5625 + x = -6.731746152 Solving 0.5625 + x = -6.731746152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + x = -6.731746152 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = -6.731746152 + -0.5625 x = -6.731746152 + -0.5625 Combine like terms: -6.731746152 + -0.5625 = -7.294246152 x = -7.294246152 Simplifying x = -7.294246152Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.169246152, -7.294246152}Solution
x = {6.169246152, -7.294246152}
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