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Simplifying (5x2 + 4x + -4) + (4x2 + 2x + -8) = 0 Reorder the terms: (-4 + 4x + 5x2) + (4x2 + 2x + -8) = 0 Remove parenthesis around (-4 + 4x + 5x2) -4 + 4x + 5x2 + (4x2 + 2x + -8) = 0 Reorder the terms: -4 + 4x + 5x2 + (-8 + 2x + 4x2) = 0 Remove parenthesis around (-8 + 2x + 4x2) -4 + 4x + 5x2 + -8 + 2x + 4x2 = 0 Reorder the terms: -4 + -8 + 4x + 2x + 5x2 + 4x2 = 0 Combine like terms: -4 + -8 = -12 -12 + 4x + 2x + 5x2 + 4x2 = 0 Combine like terms: 4x + 2x = 6x -12 + 6x + 5x2 + 4x2 = 0 Combine like terms: 5x2 + 4x2 = 9x2 -12 + 6x + 9x2 = 0 Solving -12 + 6x + 9x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + 2x + 3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + 2x + 3x2)' equal to zero and attempt to solve: Simplifying -4 + 2x + 3x2 = 0 Solving -4 + 2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.333333333 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 0.6666666667x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 0.6666666667x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 0.6666666667x + x2 = 0 + 1.333333333 0.6666666667x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 0.6666666667x + x2 = 1.333333333 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 1.333333333 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 1.333333333 + 0.1111111112 Combine like terms: 1.333333333 + 0.1111111112 = 1.4444444442 0.1111111112 + 0.6666666667x + x2 = 1.4444444442 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 1.4444444442 Calculate the square root of the right side: 1.201850425 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 1.201850425 and -1.201850425.Subproblem 1
x + 0.3333333334 = 1.201850425 Simplifying x + 0.3333333334 = 1.201850425 Reorder the terms: 0.3333333334 + x = 1.201850425 Solving 0.3333333334 + x = 1.201850425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 1.201850425 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 1.201850425 + -0.3333333334 x = 1.201850425 + -0.3333333334 Combine like terms: 1.201850425 + -0.3333333334 = 0.8685170916 x = 0.8685170916 Simplifying x = 0.8685170916Subproblem 2
x + 0.3333333334 = -1.201850425 Simplifying x + 0.3333333334 = -1.201850425 Reorder the terms: 0.3333333334 + x = -1.201850425 Solving 0.3333333334 + x = -1.201850425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -1.201850425 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -1.201850425 + -0.3333333334 x = -1.201850425 + -0.3333333334 Combine like terms: -1.201850425 + -0.3333333334 = -1.5351837584 x = -1.5351837584 Simplifying x = -1.5351837584Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8685170916, -1.5351837584}Solution
x = {0.8685170916, -1.5351837584}
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