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Simplifying 15 = 3x2 + -2x + -39 Reorder the terms: 15 = -39 + -2x + 3x2 Solving 15 = -39 + -2x + 3x2 Solving for variable 'x'. Combine like terms: 15 + 39 = 54 54 + 2x + -3x2 = -39 + -2x + 3x2 + 39 + 2x + -3x2 Reorder the terms: 54 + 2x + -3x2 = -39 + 39 + -2x + 2x + 3x2 + -3x2 Combine like terms: -39 + 39 = 0 54 + 2x + -3x2 = 0 + -2x + 2x + 3x2 + -3x2 54 + 2x + -3x2 = -2x + 2x + 3x2 + -3x2 Combine like terms: -2x + 2x = 0 54 + 2x + -3x2 = 0 + 3x2 + -3x2 54 + 2x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 54 + 2x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -18 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + -0.6666666667x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + -0.6666666667x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -0.6666666667x + x2 = 0 + 18 -0.6666666667x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 -0.6666666667x + x2 = 18 The x term is -0.6666666667x. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667x + 0.1111111112 + x2 = 18 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 18 + 0.1111111112 Combine like terms: 18 + 0.1111111112 = 18.1111111112 0.1111111112 + -0.6666666667x + x2 = 18.1111111112 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 18.1111111112 Calculate the square root of the right side: 4.255715112 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 4.255715112 and -4.255715112.Subproblem 1
x + -0.3333333334 = 4.255715112 Simplifying x + -0.3333333334 = 4.255715112 Reorder the terms: -0.3333333334 + x = 4.255715112 Solving -0.3333333334 + x = 4.255715112 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = 4.255715112 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 4.255715112 + 0.3333333334 x = 4.255715112 + 0.3333333334 Combine like terms: 4.255715112 + 0.3333333334 = 4.5890484454 x = 4.5890484454 Simplifying x = 4.5890484454Subproblem 2
x + -0.3333333334 = -4.255715112 Simplifying x + -0.3333333334 = -4.255715112 Reorder the terms: -0.3333333334 + x = -4.255715112 Solving -0.3333333334 + x = -4.255715112 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = -4.255715112 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -4.255715112 + 0.3333333334 x = -4.255715112 + 0.3333333334 Combine like terms: -4.255715112 + 0.3333333334 = -3.9223817786 x = -3.9223817786 Simplifying x = -3.9223817786Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.5890484454, -3.9223817786}
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