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Simplifying 13x2 + 13x + -28 = 2x2 + 2 Reorder the terms: -28 + 13x + 13x2 = 2x2 + 2 Reorder the terms: -28 + 13x + 13x2 = 2 + 2x2 Solving -28 + 13x + 13x2 = 2 + 2x2 Solving for variable 'x'. Reorder the terms: -28 + -2 + 13x + 13x2 + -2x2 = 2 + 2x2 + -2 + -2x2 Combine like terms: -28 + -2 = -30 -30 + 13x + 13x2 + -2x2 = 2 + 2x2 + -2 + -2x2 Combine like terms: 13x2 + -2x2 = 11x2 -30 + 13x + 11x2 = 2 + 2x2 + -2 + -2x2 Reorder the terms: -30 + 13x + 11x2 = 2 + -2 + 2x2 + -2x2 Combine like terms: 2 + -2 = 0 -30 + 13x + 11x2 = 0 + 2x2 + -2x2 -30 + 13x + 11x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -30 + 13x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -2.727272727 + 1.181818182x + x2 = 0 Move the constant term to the right: Add '2.727272727' to each side of the equation. -2.727272727 + 1.181818182x + 2.727272727 + x2 = 0 + 2.727272727 Reorder the terms: -2.727272727 + 2.727272727 + 1.181818182x + x2 = 0 + 2.727272727 Combine like terms: -2.727272727 + 2.727272727 = 0.000000000 0.000000000 + 1.181818182x + x2 = 0 + 2.727272727 1.181818182x + x2 = 0 + 2.727272727 Combine like terms: 0 + 2.727272727 = 2.727272727 1.181818182x + x2 = 2.727272727 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 = 2.727272727 + 0.3491735538 Reorder the terms: 0.3491735538 + 1.181818182x + x2 = 2.727272727 + 0.3491735538 Combine like terms: 2.727272727 + 0.3491735538 = 3.0764462808 0.3491735538 + 1.181818182x + x2 = 3.0764462808 Factor a perfect square on the left side: (x + 0.590909091)(x + 0.590909091) = 3.0764462808 Calculate the square root of the right side: 1.753980126 Break this problem into two subproblems by setting (x + 0.590909091) equal to 1.753980126 and -1.753980126.Subproblem 1
x + 0.590909091 = 1.753980126 Simplifying x + 0.590909091 = 1.753980126 Reorder the terms: 0.590909091 + x = 1.753980126 Solving 0.590909091 + x = 1.753980126 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 = 1.753980126 + -0.590909091 Combine like terms: 0.590909091 + -0.590909091 = 0.000000000 0.000000000 + x = 1.753980126 + -0.590909091 x = 1.753980126 + -0.590909091 Combine like terms: 1.753980126 + -0.590909091 = 1.163071035 x = 1.163071035 Simplifying x = 1.163071035Subproblem 2
x + 0.590909091 = -1.753980126 Simplifying x + 0.590909091 = -1.753980126 Reorder the terms: 0.590909091 + x = -1.753980126 Solving 0.590909091 + x = -1.753980126 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 = -1.753980126 + -0.590909091 Combine like terms: 0.590909091 + -0.590909091 = 0.000000000 0.000000000 + x = -1.753980126 + -0.590909091 x = -1.753980126 + -0.590909091 Combine like terms: -1.753980126 + -0.590909091 = -2.344889217 x = -2.344889217 Simplifying x = -2.344889217Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.163071035, -2.344889217}
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