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Simplifying (4x)(4x) + -10 = 2x + 10 Remove parenthesis around (4x) 4x(4x) + -10 = 2x + 10 Remove parenthesis around (4x) 4x * 4x + -10 = 2x + 10 Reorder the terms for easier multiplication: 4 * 4x * x + -10 = 2x + 10 Multiply 4 * 4 16x * x + -10 = 2x + 10 Multiply x * x 16x2 + -10 = 2x + 10 Reorder the terms: -10 + 16x2 = 2x + 10 Reorder the terms: -10 + 16x2 = 10 + 2x Solving -10 + 16x2 = 10 + 2x Solving for variable 'x'. Reorder the terms: -10 + -10 + -2x + 16x2 = 10 + 2x + -10 + -2x Combine like terms: -10 + -10 = -20 -20 + -2x + 16x2 = 10 + 2x + -10 + -2x Reorder the terms: -20 + -2x + 16x2 = 10 + -10 + 2x + -2x Combine like terms: 10 + -10 = 0 -20 + -2x + 16x2 = 0 + 2x + -2x -20 + -2x + 16x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -20 + -2x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + -1x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10 + -1x + 8x2)' equal to zero and attempt to solve: Simplifying -10 + -1x + 8x2 = 0 Solving -10 + -1x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.25 + -0.125x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -0.125x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -0.125x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -0.125x + x2 = 0 + 1.25 -0.125x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -0.125x + x2 = 1.25 The x term is -0.125x. Take half its coefficient (-0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. -0.125x + 0.00390625 + x2 = 1.25 + 0.00390625 Reorder the terms: 0.00390625 + -0.125x + x2 = 1.25 + 0.00390625 Combine like terms: 1.25 + 0.00390625 = 1.25390625 0.00390625 + -0.125x + x2 = 1.25390625 Factor a perfect square on the left side: (x + -0.0625)(x + -0.0625) = 1.25390625 Calculate the square root of the right side: 1.119779554 Break this problem into two subproblems by setting (x + -0.0625) equal to 1.119779554 and -1.119779554.Subproblem 1
x + -0.0625 = 1.119779554 Simplifying x + -0.0625 = 1.119779554 Reorder the terms: -0.0625 + x = 1.119779554 Solving -0.0625 + x = 1.119779554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = 1.119779554 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = 1.119779554 + 0.0625 x = 1.119779554 + 0.0625 Combine like terms: 1.119779554 + 0.0625 = 1.182279554 x = 1.182279554 Simplifying x = 1.182279554Subproblem 2
x + -0.0625 = -1.119779554 Simplifying x + -0.0625 = -1.119779554 Reorder the terms: -0.0625 + x = -1.119779554 Solving -0.0625 + x = -1.119779554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = -1.119779554 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = -1.119779554 + 0.0625 x = -1.119779554 + 0.0625 Combine like terms: -1.119779554 + 0.0625 = -1.057279554 x = -1.057279554 Simplifying x = -1.057279554Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.182279554, -1.057279554}Solution
x = {1.182279554, -1.057279554}
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