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Simplifying (-8x2 + -11x + -15) + (4x2 + -12x + 13) = 0 Reorder the terms: (-15 + -11x + -8x2) + (4x2 + -12x + 13) = 0 Remove parenthesis around (-15 + -11x + -8x2) -15 + -11x + -8x2 + (4x2 + -12x + 13) = 0 Reorder the terms: -15 + -11x + -8x2 + (13 + -12x + 4x2) = 0 Remove parenthesis around (13 + -12x + 4x2) -15 + -11x + -8x2 + 13 + -12x + 4x2 = 0 Reorder the terms: -15 + 13 + -11x + -12x + -8x2 + 4x2 = 0 Combine like terms: -15 + 13 = -2 -2 + -11x + -12x + -8x2 + 4x2 = 0 Combine like terms: -11x + -12x = -23x -2 + -23x + -8x2 + 4x2 = 0 Combine like terms: -8x2 + 4x2 = -4x2 -2 + -23x + -4x2 = 0 Solving -2 + -23x + -4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + 23x + 4x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + 23x + 4x2)' equal to zero and attempt to solve: Simplifying 2 + 23x + 4x2 = 0 Solving 2 + 23x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.5 + 5.75x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 5.75x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 5.75x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 5.75x + x2 = 0 + -0.5 5.75x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 5.75x + x2 = -0.5 The x term is 5.75x. Take half its coefficient (2.875). Square it (8.265625) and add it to both sides. Add '8.265625' to each side of the equation. 5.75x + 8.265625 + x2 = -0.5 + 8.265625 Reorder the terms: 8.265625 + 5.75x + x2 = -0.5 + 8.265625 Combine like terms: -0.5 + 8.265625 = 7.765625 8.265625 + 5.75x + x2 = 7.765625 Factor a perfect square on the left side: (x + 2.875)(x + 2.875) = 7.765625 Calculate the square root of the right side: 2.786687101 Break this problem into two subproblems by setting (x + 2.875) equal to 2.786687101 and -2.786687101.Subproblem 1
x + 2.875 = 2.786687101 Simplifying x + 2.875 = 2.786687101 Reorder the terms: 2.875 + x = 2.786687101 Solving 2.875 + x = 2.786687101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.875' to each side of the equation. 2.875 + -2.875 + x = 2.786687101 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + x = 2.786687101 + -2.875 x = 2.786687101 + -2.875 Combine like terms: 2.786687101 + -2.875 = -0.088312899 x = -0.088312899 Simplifying x = -0.088312899Subproblem 2
x + 2.875 = -2.786687101 Simplifying x + 2.875 = -2.786687101 Reorder the terms: 2.875 + x = -2.786687101 Solving 2.875 + x = -2.786687101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.875' to each side of the equation. 2.875 + -2.875 + x = -2.786687101 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + x = -2.786687101 + -2.875 x = -2.786687101 + -2.875 Combine like terms: -2.786687101 + -2.875 = -5.661687101 x = -5.661687101 Simplifying x = -5.661687101Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.088312899, -5.661687101}Solution
x = {-0.088312899, -5.661687101}
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