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Simplifying 3x2 + 8x + -70 = 125 Reorder the terms: -70 + 8x + 3x2 = 125 Solving -70 + 8x + 3x2 = 125 Solving for variable 'x'. Reorder the terms: -70 + -125 + 8x + 3x2 = 125 + -125 Combine like terms: -70 + -125 = -195 -195 + 8x + 3x2 = 125 + -125 Combine like terms: 125 + -125 = 0 -195 + 8x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -65 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '65' to each side of the equation. -65 + 2.666666667x + 65 + x2 = 0 + 65 Reorder the terms: -65 + 65 + 2.666666667x + x2 = 0 + 65 Combine like terms: -65 + 65 = 0 0 + 2.666666667x + x2 = 0 + 65 2.666666667x + x2 = 0 + 65 Combine like terms: 0 + 65 = 65 2.666666667x + x2 = 65 The x term is 2.666666667x. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667x + 1.777777780 + x2 = 65 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = 65 + 1.777777780 Combine like terms: 65 + 1.777777780 = 66.77777778 1.777777780 + 2.666666667x + x2 = 66.77777778 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 66.77777778 Calculate the square root of the right side: 8.171767115 Break this problem into two subproblems by setting (x + 1.333333334) equal to 8.171767115 and -8.171767115.Subproblem 1
x + 1.333333334 = 8.171767115 Simplifying x + 1.333333334 = 8.171767115 Reorder the terms: 1.333333334 + x = 8.171767115 Solving 1.333333334 + x = 8.171767115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = 8.171767115 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 8.171767115 + -1.333333334 x = 8.171767115 + -1.333333334 Combine like terms: 8.171767115 + -1.333333334 = 6.838433781 x = 6.838433781 Simplifying x = 6.838433781Subproblem 2
x + 1.333333334 = -8.171767115 Simplifying x + 1.333333334 = -8.171767115 Reorder the terms: 1.333333334 + x = -8.171767115 Solving 1.333333334 + x = -8.171767115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = -8.171767115 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -8.171767115 + -1.333333334 x = -8.171767115 + -1.333333334 Combine like terms: -8.171767115 + -1.333333334 = -9.505100449 x = -9.505100449 Simplifying x = -9.505100449Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.838433781, -9.505100449}
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