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Simplifying 6x2 + 13x = 42.25 Reorder the terms: 13x + 6x2 = 42.25 Solving 13x + 6x2 = 42.25 Solving for variable 'x'. Reorder the terms: -42.25 + 13x + 6x2 = 42.25 + -42.25 Combine like terms: 42.25 + -42.25 = 0.00 -42.25 + 13x + 6x2 = 0.00 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -7.041666667 + 2.166666667x + x2 = 0.00 Move the constant term to the right: Add '7.041666667' to each side of the equation. -7.041666667 + 2.166666667x + 7.041666667 + x2 = 0.00 + 7.041666667 Reorder the terms: -7.041666667 + 7.041666667 + 2.166666667x + x2 = 0.00 + 7.041666667 Combine like terms: -7.041666667 + 7.041666667 = 0.000000000 0.000000000 + 2.166666667x + x2 = 0.00 + 7.041666667 2.166666667x + x2 = 0.00 + 7.041666667 Combine like terms: 0.00 + 7.041666667 = 7.041666667 2.166666667x + x2 = 7.041666667 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 = 7.041666667 + 1.173611113 Reorder the terms: 1.173611113 + 2.166666667x + x2 = 7.041666667 + 1.173611113 Combine like terms: 7.041666667 + 1.173611113 = 8.21527778 1.173611113 + 2.166666667x + x2 = 8.21527778 Factor a perfect square on the left side: (x + 1.083333334)(x + 1.083333334) = 8.21527778 Calculate the square root of the right side: 2.866230587 Break this problem into two subproblems by setting (x + 1.083333334) equal to 2.866230587 and -2.866230587.Subproblem 1
x + 1.083333334 = 2.866230587 Simplifying x + 1.083333334 = 2.866230587 Reorder the terms: 1.083333334 + x = 2.866230587 Solving 1.083333334 + x = 2.866230587 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 = 2.866230587 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + x = 2.866230587 + -1.083333334 x = 2.866230587 + -1.083333334 Combine like terms: 2.866230587 + -1.083333334 = 1.782897253 x = 1.782897253 Simplifying x = 1.782897253Subproblem 2
x + 1.083333334 = -2.866230587 Simplifying x + 1.083333334 = -2.866230587 Reorder the terms: 1.083333334 + x = -2.866230587 Solving 1.083333334 + x = -2.866230587 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 = -2.866230587 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + x = -2.866230587 + -1.083333334 x = -2.866230587 + -1.083333334 Combine like terms: -2.866230587 + -1.083333334 = -3.949563921 x = -3.949563921 Simplifying x = -3.949563921Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.782897253, -3.949563921}
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