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Simplifying 10x + 4x2 + -6 = 180 Reorder the terms: -6 + 10x + 4x2 = 180 Solving -6 + 10x + 4x2 = 180 Solving for variable 'x'. Reorder the terms: -6 + -180 + 10x + 4x2 = 180 + -180 Combine like terms: -6 + -180 = -186 -186 + 10x + 4x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -186 + 10x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-93 + 5x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-93 + 5x + 2x2)' equal to zero and attempt to solve: Simplifying -93 + 5x + 2x2 = 0 Solving -93 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -46.5 + 2.5x + x2 = 0 Move the constant term to the right: Add '46.5' to each side of the equation. -46.5 + 2.5x + 46.5 + x2 = 0 + 46.5 Reorder the terms: -46.5 + 46.5 + 2.5x + x2 = 0 + 46.5 Combine like terms: -46.5 + 46.5 = 0.0 0.0 + 2.5x + x2 = 0 + 46.5 2.5x + x2 = 0 + 46.5 Combine like terms: 0 + 46.5 = 46.5 2.5x + x2 = 46.5 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 46.5 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 46.5 + 1.5625 Combine like terms: 46.5 + 1.5625 = 48.0625 1.5625 + 2.5x + x2 = 48.0625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 48.0625 Calculate the square root of the right side: 6.932712312 Break this problem into two subproblems by setting (x + 1.25) equal to 6.932712312 and -6.932712312.Subproblem 1
x + 1.25 = 6.932712312 Simplifying x + 1.25 = 6.932712312 Reorder the terms: 1.25 + x = 6.932712312 Solving 1.25 + x = 6.932712312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 6.932712312 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 6.932712312 + -1.25 x = 6.932712312 + -1.25 Combine like terms: 6.932712312 + -1.25 = 5.682712312 x = 5.682712312 Simplifying x = 5.682712312Subproblem 2
x + 1.25 = -6.932712312 Simplifying x + 1.25 = -6.932712312 Reorder the terms: 1.25 + x = -6.932712312 Solving 1.25 + x = -6.932712312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -6.932712312 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -6.932712312 + -1.25 x = -6.932712312 + -1.25 Combine like terms: -6.932712312 + -1.25 = -8.182712312 x = -8.182712312 Simplifying x = -8.182712312Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.682712312, -8.182712312}Solution
x = {5.682712312, -8.182712312}
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