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Simplifying 3x + -2(5x + -4) = 4x(-2x + -26) Reorder the terms: 3x + -2(-4 + 5x) = 4x(-2x + -26) 3x + (-4 * -2 + 5x * -2) = 4x(-2x + -26) 3x + (8 + -10x) = 4x(-2x + -26) Reorder the terms: 8 + 3x + -10x = 4x(-2x + -26) Combine like terms: 3x + -10x = -7x 8 + -7x = 4x(-2x + -26) Reorder the terms: 8 + -7x = 4x(-26 + -2x) 8 + -7x = (-26 * 4x + -2x * 4x) 8 + -7x = (-104x + -8x2) Solving 8 + -7x = -104x + -8x2 Solving for variable 'x'. Combine like terms: -7x + 104x = 97x 8 + 97x + 8x2 = -104x + -8x2 + 104x + 8x2 Reorder the terms: 8 + 97x + 8x2 = -104x + 104x + -8x2 + 8x2 Combine like terms: -104x + 104x = 0 8 + 97x + 8x2 = 0 + -8x2 + 8x2 8 + 97x + 8x2 = -8x2 + 8x2 Combine like terms: -8x2 + 8x2 = 0 8 + 97x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1 + 12.125x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 12.125x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 12.125x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 12.125x + x2 = 0 + -1 12.125x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 12.125x + x2 = -1 The x term is 12.125x. Take half its coefficient (6.0625). Square it (36.75390625) and add it to both sides. Add '36.75390625' to each side of the equation. 12.125x + 36.75390625 + x2 = -1 + 36.75390625 Reorder the terms: 36.75390625 + 12.125x + x2 = -1 + 36.75390625 Combine like terms: -1 + 36.75390625 = 35.75390625 36.75390625 + 12.125x + x2 = 35.75390625 Factor a perfect square on the left side: (x + 6.0625)(x + 6.0625) = 35.75390625 Calculate the square root of the right side: 5.97945702 Break this problem into two subproblems by setting (x + 6.0625) equal to 5.97945702 and -5.97945702.Subproblem 1
x + 6.0625 = 5.97945702 Simplifying x + 6.0625 = 5.97945702 Reorder the terms: 6.0625 + x = 5.97945702 Solving 6.0625 + x = 5.97945702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.0625' to each side of the equation. 6.0625 + -6.0625 + x = 5.97945702 + -6.0625 Combine like terms: 6.0625 + -6.0625 = 0.0000 0.0000 + x = 5.97945702 + -6.0625 x = 5.97945702 + -6.0625 Combine like terms: 5.97945702 + -6.0625 = -0.08304298 x = -0.08304298 Simplifying x = -0.08304298Subproblem 2
x + 6.0625 = -5.97945702 Simplifying x + 6.0625 = -5.97945702 Reorder the terms: 6.0625 + x = -5.97945702 Solving 6.0625 + x = -5.97945702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.0625' to each side of the equation. 6.0625 + -6.0625 + x = -5.97945702 + -6.0625 Combine like terms: 6.0625 + -6.0625 = 0.0000 0.0000 + x = -5.97945702 + -6.0625 x = -5.97945702 + -6.0625 Combine like terms: -5.97945702 + -6.0625 = -12.04195702 x = -12.04195702 Simplifying x = -12.04195702Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.08304298, -12.04195702}
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