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Simplifying 133 = -6x + 7x(x + 18) Reorder the terms: 133 = -6x + 7x(18 + x) 133 = -6x + (18 * 7x + x * 7x) 133 = -6x + (126x + 7x2) Combine like terms: -6x + 126x = 120x 133 = 120x + 7x2 Solving 133 = 120x + 7x2 Solving for variable 'x'. Reorder the terms: 133 + -120x + -7x2 = 120x + -120x + 7x2 + -7x2 Combine like terms: 120x + -120x = 0 133 + -120x + -7x2 = 0 + 7x2 + -7x2 133 + -120x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 133 + -120x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -19 + 17.14285714x + x2 = 0 Move the constant term to the right: Add '19' to each side of the equation. -19 + 17.14285714x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + 17.14285714x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 17.14285714x + x2 = 0 + 19 17.14285714x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 17.14285714x + x2 = 19 The x term is 17.14285714x. Take half its coefficient (8.57142857). Square it (73.46938773) and add it to both sides. Add '73.46938773' to each side of the equation. 17.14285714x + 73.46938773 + x2 = 19 + 73.46938773 Reorder the terms: 73.46938773 + 17.14285714x + x2 = 19 + 73.46938773 Combine like terms: 19 + 73.46938773 = 92.46938773 73.46938773 + 17.14285714x + x2 = 92.46938773 Factor a perfect square on the left side: (x + 8.57142857)(x + 8.57142857) = 92.46938773 Calculate the square root of the right side: 9.616100443 Break this problem into two subproblems by setting (x + 8.57142857) equal to 9.616100443 and -9.616100443.Subproblem 1
x + 8.57142857 = 9.616100443 Simplifying x + 8.57142857 = 9.616100443 Reorder the terms: 8.57142857 + x = 9.616100443 Solving 8.57142857 + x = 9.616100443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.57142857' to each side of the equation. 8.57142857 + -8.57142857 + x = 9.616100443 + -8.57142857 Combine like terms: 8.57142857 + -8.57142857 = 0.00000000 0.00000000 + x = 9.616100443 + -8.57142857 x = 9.616100443 + -8.57142857 Combine like terms: 9.616100443 + -8.57142857 = 1.044671873 x = 1.044671873 Simplifying x = 1.044671873Subproblem 2
x + 8.57142857 = -9.616100443 Simplifying x + 8.57142857 = -9.616100443 Reorder the terms: 8.57142857 + x = -9.616100443 Solving 8.57142857 + x = -9.616100443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.57142857' to each side of the equation. 8.57142857 + -8.57142857 + x = -9.616100443 + -8.57142857 Combine like terms: 8.57142857 + -8.57142857 = 0.00000000 0.00000000 + x = -9.616100443 + -8.57142857 x = -9.616100443 + -8.57142857 Combine like terms: -9.616100443 + -8.57142857 = -18.187529013 x = -18.187529013 Simplifying x = -18.187529013Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.044671873, -18.187529013}
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