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Simplifying 2x * 2x + 5x + -2 = 126 Reorder the terms for easier multiplication: 2 * 2x * x + 5x + -2 = 126 Multiply 2 * 2 4x * x + 5x + -2 = 126 Multiply x * x 4x2 + 5x + -2 = 126 Reorder the terms: -2 + 5x + 4x2 = 126 Solving -2 + 5x + 4x2 = 126 Solving for variable 'x'. Reorder the terms: -2 + -126 + 5x + 4x2 = 126 + -126 Combine like terms: -2 + -126 = -128 -128 + 5x + 4x2 = 126 + -126 Combine like terms: 126 + -126 = 0 -128 + 5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -32 + 1.25x + x2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + 1.25x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + 1.25x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 1.25x + x2 = 0 + 32 1.25x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 1.25x + x2 = 32 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 32 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 32 + 0.390625 Combine like terms: 32 + 0.390625 = 32.390625 0.390625 + 1.25x + x2 = 32.390625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 32.390625 Calculate the square root of the right side: 5.691276219 Break this problem into two subproblems by setting (x + 0.625) equal to 5.691276219 and -5.691276219.Subproblem 1
x + 0.625 = 5.691276219 Simplifying x + 0.625 = 5.691276219 Reorder the terms: 0.625 + x = 5.691276219 Solving 0.625 + x = 5.691276219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 5.691276219 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 5.691276219 + -0.625 x = 5.691276219 + -0.625 Combine like terms: 5.691276219 + -0.625 = 5.066276219 x = 5.066276219 Simplifying x = 5.066276219Subproblem 2
x + 0.625 = -5.691276219 Simplifying x + 0.625 = -5.691276219 Reorder the terms: 0.625 + x = -5.691276219 Solving 0.625 + x = -5.691276219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -5.691276219 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -5.691276219 + -0.625 x = -5.691276219 + -0.625 Combine like terms: -5.691276219 + -0.625 = -6.316276219 x = -6.316276219 Simplifying x = -6.316276219Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.066276219, -6.316276219}
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