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Simplifying 19x * x + -9x + -100 = 135 Multiply x * x 19x2 + -9x + -100 = 135 Reorder the terms: -100 + -9x + 19x2 = 135 Solving -100 + -9x + 19x2 = 135 Solving for variable 'x'. Reorder the terms: -100 + -135 + -9x + 19x2 = 135 + -135 Combine like terms: -100 + -135 = -235 -235 + -9x + 19x2 = 135 + -135 Combine like terms: 135 + -135 = 0 -235 + -9x + 19x2 = 0 Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. -12.36842105 + -0.4736842105x + x2 = 0 Move the constant term to the right: Add '12.36842105' to each side of the equation. -12.36842105 + -0.4736842105x + 12.36842105 + x2 = 0 + 12.36842105 Reorder the terms: -12.36842105 + 12.36842105 + -0.4736842105x + x2 = 0 + 12.36842105 Combine like terms: -12.36842105 + 12.36842105 = 0.00000000 0.00000000 + -0.4736842105x + x2 = 0 + 12.36842105 -0.4736842105x + x2 = 0 + 12.36842105 Combine like terms: 0 + 12.36842105 = 12.36842105 -0.4736842105x + x2 = 12.36842105 The x term is -0.4736842105x. Take half its coefficient (-0.2368421053). Square it (0.05609418284) and add it to both sides. Add '0.05609418284' to each side of the equation. -0.4736842105x + 0.05609418284 + x2 = 12.36842105 + 0.05609418284 Reorder the terms: 0.05609418284 + -0.4736842105x + x2 = 12.36842105 + 0.05609418284 Combine like terms: 12.36842105 + 0.05609418284 = 12.42451523284 0.05609418284 + -0.4736842105x + x2 = 12.42451523284 Factor a perfect square on the left side: (x + -0.2368421053)(x + -0.2368421053) = 12.42451523284 Calculate the square root of the right side: 3.524842583 Break this problem into two subproblems by setting (x + -0.2368421053) equal to 3.524842583 and -3.524842583.Subproblem 1
x + -0.2368421053 = 3.524842583 Simplifying x + -0.2368421053 = 3.524842583 Reorder the terms: -0.2368421053 + x = 3.524842583 Solving -0.2368421053 + x = 3.524842583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2368421053' to each side of the equation. -0.2368421053 + 0.2368421053 + x = 3.524842583 + 0.2368421053 Combine like terms: -0.2368421053 + 0.2368421053 = 0.0000000000 0.0000000000 + x = 3.524842583 + 0.2368421053 x = 3.524842583 + 0.2368421053 Combine like terms: 3.524842583 + 0.2368421053 = 3.7616846883 x = 3.7616846883 Simplifying x = 3.7616846883Subproblem 2
x + -0.2368421053 = -3.524842583 Simplifying x + -0.2368421053 = -3.524842583 Reorder the terms: -0.2368421053 + x = -3.524842583 Solving -0.2368421053 + x = -3.524842583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2368421053' to each side of the equation. -0.2368421053 + 0.2368421053 + x = -3.524842583 + 0.2368421053 Combine like terms: -0.2368421053 + 0.2368421053 = 0.0000000000 0.0000000000 + x = -3.524842583 + 0.2368421053 x = -3.524842583 + 0.2368421053 Combine like terms: -3.524842583 + 0.2368421053 = -3.2880004777 x = -3.2880004777 Simplifying x = -3.2880004777Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.7616846883, -3.2880004777}
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