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Simplifying 6x2 + 13x + -63 = 63 Reorder the terms: -63 + 13x + 6x2 = 63 Solving -63 + 13x + 6x2 = 63 Solving for variable 'x'. Reorder the terms: -63 + -63 + 13x + 6x2 = 63 + -63 Combine like terms: -63 + -63 = -126 -126 + 13x + 6x2 = 63 + -63 Combine like terms: 63 + -63 = 0 -126 + 13x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -21 + 2.166666667x + x2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + 2.166666667x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + 2.166666667x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 2.166666667x + x2 = 0 + 21 2.166666667x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 2.166666667x + x2 = 21 The x term is 2.166666667x. Take half its coefficient (1.083333334). Square it (1.173611113) and add it to both sides. Add '1.173611113' to each side of the equation. 2.166666667x + 1.173611113 + x2 = 21 + 1.173611113 Reorder the terms: 1.173611113 + 2.166666667x + x2 = 21 + 1.173611113 Combine like terms: 21 + 1.173611113 = 22.173611113 1.173611113 + 2.166666667x + x2 = 22.173611113 Factor a perfect square on the left side: (x + 1.083333334)(x + 1.083333334) = 22.173611113 Calculate the square root of the right side: 4.708886398 Break this problem into two subproblems by setting (x + 1.083333334) equal to 4.708886398 and -4.708886398.Subproblem 1
x + 1.083333334 = 4.708886398 Simplifying x + 1.083333334 = 4.708886398 Reorder the terms: 1.083333334 + x = 4.708886398 Solving 1.083333334 + x = 4.708886398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.083333334' to each side of the equation. 1.083333334 + -1.083333334 + x = 4.708886398 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + x = 4.708886398 + -1.083333334 x = 4.708886398 + -1.083333334 Combine like terms: 4.708886398 + -1.083333334 = 3.625553064 x = 3.625553064 Simplifying x = 3.625553064Subproblem 2
x + 1.083333334 = -4.708886398 Simplifying x + 1.083333334 = -4.708886398 Reorder the terms: 1.083333334 + x = -4.708886398 Solving 1.083333334 + x = -4.708886398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.083333334' to each side of the equation. 1.083333334 + -1.083333334 + x = -4.708886398 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + x = -4.708886398 + -1.083333334 x = -4.708886398 + -1.083333334 Combine like terms: -4.708886398 + -1.083333334 = -5.792219732 x = -5.792219732 Simplifying x = -5.792219732Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.625553064, -5.792219732}
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