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Simplifying (8x2 + 5x + -9) + (3x2 + 8x) = 0 Reorder the terms: (-9 + 5x + 8x2) + (3x2 + 8x) = 0 Remove parenthesis around (-9 + 5x + 8x2) -9 + 5x + 8x2 + (3x2 + 8x) = 0 Reorder the terms: -9 + 5x + 8x2 + (8x + 3x2) = 0 Remove parenthesis around (8x + 3x2) -9 + 5x + 8x2 + 8x + 3x2 = 0 Reorder the terms: -9 + 5x + 8x + 8x2 + 3x2 = 0 Combine like terms: 5x + 8x = 13x -9 + 13x + 8x2 + 3x2 = 0 Combine like terms: 8x2 + 3x2 = 11x2 -9 + 13x + 11x2 = 0 Solving -9 + 13x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.8181818182 + 1.181818182x + x2 = 0 Move the constant term to the right: Add '0.8181818182' to each side of the equation. -0.8181818182 + 1.181818182x + 0.8181818182 + x2 = 0 + 0.8181818182 Reorder the terms: -0.8181818182 + 0.8181818182 + 1.181818182x + x2 = 0 + 0.8181818182 Combine like terms: -0.8181818182 + 0.8181818182 = 0.0000000000 0.0000000000 + 1.181818182x + x2 = 0 + 0.8181818182 1.181818182x + x2 = 0 + 0.8181818182 Combine like terms: 0 + 0.8181818182 = 0.8181818182 1.181818182x + x2 = 0.8181818182 The x term is 1.181818182x. Take half its coefficient (0.590909091). Square it (0.3491735538) and add it to both sides. Add '0.3491735538' to each side of the equation. 1.181818182x + 0.3491735538 + x2 = 0.8181818182 + 0.3491735538 Reorder the terms: 0.3491735538 + 1.181818182x + x2 = 0.8181818182 + 0.3491735538 Combine like terms: 0.8181818182 + 0.3491735538 = 1.167355372 0.3491735538 + 1.181818182x + x2 = 1.167355372 Factor a perfect square on the left side: (x + 0.590909091)(x + 0.590909091) = 1.167355372 Calculate the square root of the right side: 1.080442211 Break this problem into two subproblems by setting (x + 0.590909091) equal to 1.080442211 and -1.080442211.Subproblem 1
x + 0.590909091 = 1.080442211 Simplifying x + 0.590909091 = 1.080442211 Reorder the terms: 0.590909091 + x = 1.080442211 Solving 0.590909091 + x = 1.080442211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.590909091' to each side of the equation. 0.590909091 + -0.590909091 + x = 1.080442211 + -0.590909091 Combine like terms: 0.590909091 + -0.590909091 = 0.000000000 0.000000000 + x = 1.080442211 + -0.590909091 x = 1.080442211 + -0.590909091 Combine like terms: 1.080442211 + -0.590909091 = 0.48953312 x = 0.48953312 Simplifying x = 0.48953312Subproblem 2
x + 0.590909091 = -1.080442211 Simplifying x + 0.590909091 = -1.080442211 Reorder the terms: 0.590909091 + x = -1.080442211 Solving 0.590909091 + x = -1.080442211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.590909091' to each side of the equation. 0.590909091 + -0.590909091 + x = -1.080442211 + -0.590909091 Combine like terms: 0.590909091 + -0.590909091 = 0.000000000 0.000000000 + x = -1.080442211 + -0.590909091 x = -1.080442211 + -0.590909091 Combine like terms: -1.080442211 + -0.590909091 = -1.671351302 x = -1.671351302 Simplifying x = -1.671351302Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.48953312, -1.671351302}
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