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Simplifying 7x2 + -10 + 6x2 + -3x = 180 Reorder the terms: -10 + -3x + 7x2 + 6x2 = 180 Combine like terms: 7x2 + 6x2 = 13x2 -10 + -3x + 13x2 = 180 Solving -10 + -3x + 13x2 = 180 Solving for variable 'x'. Reorder the terms: -10 + -180 + -3x + 13x2 = 180 + -180 Combine like terms: -10 + -180 = -190 -190 + -3x + 13x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -190 + -3x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -14.61538462 + -0.2307692308x + x2 = 0 Move the constant term to the right: Add '14.61538462' to each side of the equation. -14.61538462 + -0.2307692308x + 14.61538462 + x2 = 0 + 14.61538462 Reorder the terms: -14.61538462 + 14.61538462 + -0.2307692308x + x2 = 0 + 14.61538462 Combine like terms: -14.61538462 + 14.61538462 = 0.00000000 0.00000000 + -0.2307692308x + x2 = 0 + 14.61538462 -0.2307692308x + x2 = 0 + 14.61538462 Combine like terms: 0 + 14.61538462 = 14.61538462 -0.2307692308x + x2 = 14.61538462 The x term is -0.2307692308x. Take half its coefficient (-0.1153846154). Square it (0.01331360947) and add it to both sides. Add '0.01331360947' to each side of the equation. -0.2307692308x + 0.01331360947 + x2 = 14.61538462 + 0.01331360947 Reorder the terms: 0.01331360947 + -0.2307692308x + x2 = 14.61538462 + 0.01331360947 Combine like terms: 14.61538462 + 0.01331360947 = 14.62869822947 0.01331360947 + -0.2307692308x + x2 = 14.62869822947 Factor a perfect square on the left side: (x + -0.1153846154)(x + -0.1153846154) = 14.62869822947 Calculate the square root of the right side: 3.824748126 Break this problem into two subproblems by setting (x + -0.1153846154) equal to 3.824748126 and -3.824748126.Subproblem 1
x + -0.1153846154 = 3.824748126 Simplifying x + -0.1153846154 = 3.824748126 Reorder the terms: -0.1153846154 + x = 3.824748126 Solving -0.1153846154 + x = 3.824748126 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1153846154' to each side of the equation. -0.1153846154 + 0.1153846154 + x = 3.824748126 + 0.1153846154 Combine like terms: -0.1153846154 + 0.1153846154 = 0.0000000000 0.0000000000 + x = 3.824748126 + 0.1153846154 x = 3.824748126 + 0.1153846154 Combine like terms: 3.824748126 + 0.1153846154 = 3.9401327414 x = 3.9401327414 Simplifying x = 3.9401327414Subproblem 2
x + -0.1153846154 = -3.824748126 Simplifying x + -0.1153846154 = -3.824748126 Reorder the terms: -0.1153846154 + x = -3.824748126 Solving -0.1153846154 + x = -3.824748126 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1153846154' to each side of the equation. -0.1153846154 + 0.1153846154 + x = -3.824748126 + 0.1153846154 Combine like terms: -0.1153846154 + 0.1153846154 = 0.0000000000 0.0000000000 + x = -3.824748126 + 0.1153846154 x = -3.824748126 + 0.1153846154 Combine like terms: -3.824748126 + 0.1153846154 = -3.7093635106 x = -3.7093635106 Simplifying x = -3.7093635106Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.9401327414, -3.7093635106}
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