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Simplifying 4x2 + -8x + 4 = 36(-5x + -3) Reorder the terms: 4 + -8x + 4x2 = 36(-5x + -3) Reorder the terms: 4 + -8x + 4x2 = 36(-3 + -5x) 4 + -8x + 4x2 = (-3 * 36 + -5x * 36) 4 + -8x + 4x2 = (-108 + -180x) Solving 4 + -8x + 4x2 = -108 + -180x Solving for variable 'x'. Reorder the terms: 4 + 108 + -8x + 180x + 4x2 = -108 + -180x + 108 + 180x Combine like terms: 4 + 108 = 112 112 + -8x + 180x + 4x2 = -108 + -180x + 108 + 180x Combine like terms: -8x + 180x = 172x 112 + 172x + 4x2 = -108 + -180x + 108 + 180x Reorder the terms: 112 + 172x + 4x2 = -108 + 108 + -180x + 180x Combine like terms: -108 + 108 = 0 112 + 172x + 4x2 = 0 + -180x + 180x 112 + 172x + 4x2 = -180x + 180x Combine like terms: -180x + 180x = 0 112 + 172x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(28 + 43x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(28 + 43x + x2)' equal to zero and attempt to solve: Simplifying 28 + 43x + x2 = 0 Solving 28 + 43x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-28' to each side of the equation. 28 + 43x + -28 + x2 = 0 + -28 Reorder the terms: 28 + -28 + 43x + x2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + 43x + x2 = 0 + -28 43x + x2 = 0 + -28 Combine like terms: 0 + -28 = -28 43x + x2 = -28 The x term is 43x. Take half its coefficient (21.5). Square it (462.25) and add it to both sides. Add '462.25' to each side of the equation. 43x + 462.25 + x2 = -28 + 462.25 Reorder the terms: 462.25 + 43x + x2 = -28 + 462.25 Combine like terms: -28 + 462.25 = 434.25 462.25 + 43x + x2 = 434.25 Factor a perfect square on the left side: (x + 21.5)(x + 21.5) = 434.25 Calculate the square root of the right side: 20.838665984 Break this problem into two subproblems by setting (x + 21.5) equal to 20.838665984 and -20.838665984.Subproblem 1
x + 21.5 = 20.838665984 Simplifying x + 21.5 = 20.838665984 Reorder the terms: 21.5 + x = 20.838665984 Solving 21.5 + x = 20.838665984 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21.5' to each side of the equation. 21.5 + -21.5 + x = 20.838665984 + -21.5 Combine like terms: 21.5 + -21.5 = 0.0 0.0 + x = 20.838665984 + -21.5 x = 20.838665984 + -21.5 Combine like terms: 20.838665984 + -21.5 = -0.661334016 x = -0.661334016 Simplifying x = -0.661334016Subproblem 2
x + 21.5 = -20.838665984 Simplifying x + 21.5 = -20.838665984 Reorder the terms: 21.5 + x = -20.838665984 Solving 21.5 + x = -20.838665984 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21.5' to each side of the equation. 21.5 + -21.5 + x = -20.838665984 + -21.5 Combine like terms: 21.5 + -21.5 = 0.0 0.0 + x = -20.838665984 + -21.5 x = -20.838665984 + -21.5 Combine like terms: -20.838665984 + -21.5 = -42.338665984 x = -42.338665984 Simplifying x = -42.338665984Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.661334016, -42.338665984}Solution
x = {-0.661334016, -42.338665984}
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