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Simplifying 4x * 4x + 2x + -7 = 0 Reorder the terms for easier multiplication: 4 * 4x * x + 2x + -7 = 0 Multiply 4 * 4 16x * x + 2x + -7 = 0 Multiply x * x 16x2 + 2x + -7 = 0 Reorder the terms: -7 + 2x + 16x2 = 0 Solving -7 + 2x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.4375 + 0.125x + x2 = 0 Move the constant term to the right: Add '0.4375' to each side of the equation. -0.4375 + 0.125x + 0.4375 + x2 = 0 + 0.4375 Reorder the terms: -0.4375 + 0.4375 + 0.125x + x2 = 0 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + 0.125x + x2 = 0 + 0.4375 0.125x + x2 = 0 + 0.4375 Combine like terms: 0 + 0.4375 = 0.4375 0.125x + x2 = 0.4375 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 = 0.4375 + 0.00390625 Reorder the terms: 0.00390625 + 0.125x + x2 = 0.4375 + 0.00390625 Combine like terms: 0.4375 + 0.00390625 = 0.44140625 0.00390625 + 0.125x + x2 = 0.44140625 Factor a perfect square on the left side: (x + 0.0625)(x + 0.0625) = 0.44140625 Calculate the square root of the right side: 0.664384113 Break this problem into two subproblems by setting (x + 0.0625) equal to 0.664384113 and -0.664384113.Subproblem 1
x + 0.0625 = 0.664384113 Simplifying x + 0.0625 = 0.664384113 Reorder the terms: 0.0625 + x = 0.664384113 Solving 0.0625 + x = 0.664384113 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 = 0.664384113 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + x = 0.664384113 + -0.0625 x = 0.664384113 + -0.0625 Combine like terms: 0.664384113 + -0.0625 = 0.601884113 x = 0.601884113 Simplifying x = 0.601884113Subproblem 2
x + 0.0625 = -0.664384113 Simplifying x + 0.0625 = -0.664384113 Reorder the terms: 0.0625 + x = -0.664384113 Solving 0.0625 + x = -0.664384113 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 = -0.664384113 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + x = -0.664384113 + -0.0625 x = -0.664384113 + -0.0625 Combine like terms: -0.664384113 + -0.0625 = -0.726884113 x = -0.726884113 Simplifying x = -0.726884113Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.601884113, -0.726884113}
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