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Simplifying 10x + 4x2 + -6 = 90 Reorder the terms: -6 + 10x + 4x2 = 90 Solving -6 + 10x + 4x2 = 90 Solving for variable 'x'. Reorder the terms: -6 + -90 + 10x + 4x2 = 90 + -90 Combine like terms: -6 + -90 = -96 -96 + 10x + 4x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -96 + 10x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-48 + 5x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-48 + 5x + 2x2)' equal to zero and attempt to solve: Simplifying -48 + 5x + 2x2 = 0 Solving -48 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -24 + 2.5x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + 2.5x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 2.5x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 2.5x + x2 = 0 + 24 2.5x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 2.5x + x2 = 24 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 = 24 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 24 + 1.5625 Combine like terms: 24 + 1.5625 = 25.5625 1.5625 + 2.5x + x2 = 25.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 25.5625 Calculate the square root of the right side: 5.055937104 Break this problem into two subproblems by setting (x + 1.25) equal to 5.055937104 and -5.055937104.Subproblem 1
x + 1.25 = 5.055937104 Simplifying x + 1.25 = 5.055937104 Reorder the terms: 1.25 + x = 5.055937104 Solving 1.25 + x = 5.055937104 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 = 5.055937104 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 5.055937104 + -1.25 x = 5.055937104 + -1.25 Combine like terms: 5.055937104 + -1.25 = 3.805937104 x = 3.805937104 Simplifying x = 3.805937104Subproblem 2
x + 1.25 = -5.055937104 Simplifying x + 1.25 = -5.055937104 Reorder the terms: 1.25 + x = -5.055937104 Solving 1.25 + x = -5.055937104 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 = -5.055937104 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -5.055937104 + -1.25 x = -5.055937104 + -1.25 Combine like terms: -5.055937104 + -1.25 = -6.305937104 x = -6.305937104 Simplifying x = -6.305937104Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.805937104, -6.305937104}Solution
x = {3.805937104, -6.305937104}
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