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Simplifying 4x + -1(3 + 5x) + -7 = -4x * 2x + -6 4x + (3 * -1 + 5x * -1) + -7 = -4x * 2x + -6 4x + (-3 + -5x) + -7 = -4x * 2x + -6 Reorder the terms: -3 + -7 + 4x + -5x = -4x * 2x + -6 Combine like terms: -3 + -7 = -10 -10 + 4x + -5x = -4x * 2x + -6 Combine like terms: 4x + -5x = -1x -10 + -1x = -4x * 2x + -6 Reorder the terms for easier multiplication: -10 + -1x = -4 * 2x * x + -6 Multiply -4 * 2 -10 + -1x = -8x * x + -6 Multiply x * x -10 + -1x = -8x2 + -6 Reorder the terms: -10 + -1x = -6 + -8x2 Solving -10 + -1x = -6 + -8x2 Solving for variable 'x'. Reorder the terms: -10 + 6 + -1x + 8x2 = -6 + -8x2 + 6 + 8x2 Combine like terms: -10 + 6 = -4 -4 + -1x + 8x2 = -6 + -8x2 + 6 + 8x2 Reorder the terms: -4 + -1x + 8x2 = -6 + 6 + -8x2 + 8x2 Combine like terms: -6 + 6 = 0 -4 + -1x + 8x2 = 0 + -8x2 + 8x2 -4 + -1x + 8x2 = -8x2 + 8x2 Combine like terms: -8x2 + 8x2 = 0 -4 + -1x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.5 + -0.125x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.125x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.125x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.125x + x2 = 0 + 0.5 -0.125x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -0.125x + x2 = 0.5 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 = 0.5 + 0.00390625 Reorder the terms: 0.00390625 + -0.125x + x2 = 0.5 + 0.00390625 Combine like terms: 0.5 + 0.00390625 = 0.50390625 0.00390625 + -0.125x + x2 = 0.50390625 Factor a perfect square on the left side: (x + -0.0625)(x + -0.0625) = 0.50390625 Calculate the square root of the right side: 0.709863543 Break this problem into two subproblems by setting (x + -0.0625) equal to 0.709863543 and -0.709863543.Subproblem 1
x + -0.0625 = 0.709863543 Simplifying x + -0.0625 = 0.709863543 Reorder the terms: -0.0625 + x = 0.709863543 Solving -0.0625 + x = 0.709863543 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 = 0.709863543 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = 0.709863543 + 0.0625 x = 0.709863543 + 0.0625 Combine like terms: 0.709863543 + 0.0625 = 0.772363543 x = 0.772363543 Simplifying x = 0.772363543Subproblem 2
x + -0.0625 = -0.709863543 Simplifying x + -0.0625 = -0.709863543 Reorder the terms: -0.0625 + x = -0.709863543 Solving -0.0625 + x = -0.709863543 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 = -0.709863543 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = -0.709863543 + 0.0625 x = -0.709863543 + 0.0625 Combine like terms: -0.709863543 + 0.0625 = -0.647363543 x = -0.647363543 Simplifying x = -0.647363543Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.772363543, -0.647363543}
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