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Simplifying 0 = 11x2 + -13x + -306 Reorder the terms: 0 = -306 + -13x + 11x2 Solving 0 = -306 + -13x + 11x2 Solving for variable 'x'. Combine like terms: 0 + 306 = 306 306 + 13x + -11x2 = -306 + -13x + 11x2 + 306 + 13x + -11x2 Reorder the terms: 306 + 13x + -11x2 = -306 + 306 + -13x + 13x + 11x2 + -11x2 Combine like terms: -306 + 306 = 0 306 + 13x + -11x2 = 0 + -13x + 13x + 11x2 + -11x2 306 + 13x + -11x2 = -13x + 13x + 11x2 + -11x2 Combine like terms: -13x + 13x = 0 306 + 13x + -11x2 = 0 + 11x2 + -11x2 306 + 13x + -11x2 = 11x2 + -11x2 Combine like terms: 11x2 + -11x2 = 0 306 + 13x + -11x2 = 0 Begin completing the square. Divide all terms by -11 the coefficient of the squared term: Divide each side by '-11'. -27.81818182 + -1.181818182x + x2 = 0 Move the constant term to the right: Add '27.81818182' to each side of the equation. -27.81818182 + -1.181818182x + 27.81818182 + x2 = 0 + 27.81818182 Reorder the terms: -27.81818182 + 27.81818182 + -1.181818182x + x2 = 0 + 27.81818182 Combine like terms: -27.81818182 + 27.81818182 = 0.00000000 0.00000000 + -1.181818182x + x2 = 0 + 27.81818182 -1.181818182x + x2 = 0 + 27.81818182 Combine like terms: 0 + 27.81818182 = 27.81818182 -1.181818182x + x2 = 27.81818182 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 = 27.81818182 + 0.3491735538 Reorder the terms: 0.3491735538 + -1.181818182x + x2 = 27.81818182 + 0.3491735538 Combine like terms: 27.81818182 + 0.3491735538 = 28.1673553738 0.3491735538 + -1.181818182x + x2 = 28.1673553738 Factor a perfect square on the left side: (x + -0.590909091)(x + -0.590909091) = 28.1673553738 Calculate the square root of the right side: 5.30729266 Break this problem into two subproblems by setting (x + -0.590909091) equal to 5.30729266 and -5.30729266.Subproblem 1
x + -0.590909091 = 5.30729266 Simplifying x + -0.590909091 = 5.30729266 Reorder the terms: -0.590909091 + x = 5.30729266 Solving -0.590909091 + x = 5.30729266 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 = 5.30729266 + 0.590909091 Combine like terms: -0.590909091 + 0.590909091 = 0.000000000 0.000000000 + x = 5.30729266 + 0.590909091 x = 5.30729266 + 0.590909091 Combine like terms: 5.30729266 + 0.590909091 = 5.898201751 x = 5.898201751 Simplifying x = 5.898201751Subproblem 2
x + -0.590909091 = -5.30729266 Simplifying x + -0.590909091 = -5.30729266 Reorder the terms: -0.590909091 + x = -5.30729266 Solving -0.590909091 + x = -5.30729266 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 = -5.30729266 + 0.590909091 Combine like terms: -0.590909091 + 0.590909091 = 0.000000000 0.000000000 + x = -5.30729266 + 0.590909091 x = -5.30729266 + 0.590909091 Combine like terms: -5.30729266 + 0.590909091 = -4.716383569 x = -4.716383569 Simplifying x = -4.716383569Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.898201751, -4.716383569}
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