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Simplifying 2x2 + 26x2 + -18x + -234 = 3 Reorder the terms: -234 + -18x + 2x2 + 26x2 = 3 Combine like terms: 2x2 + 26x2 = 28x2 -234 + -18x + 28x2 = 3 Solving -234 + -18x + 28x2 = 3 Solving for variable 'x'. Reorder the terms: -234 + -3 + -18x + 28x2 = 3 + -3 Combine like terms: -234 + -3 = -237 -237 + -18x + 28x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -237 + -18x + 28x2 = 0 Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -8.464285714 + -0.6428571429x + x2 = 0 Move the constant term to the right: Add '8.464285714' to each side of the equation. -8.464285714 + -0.6428571429x + 8.464285714 + x2 = 0 + 8.464285714 Reorder the terms: -8.464285714 + 8.464285714 + -0.6428571429x + x2 = 0 + 8.464285714 Combine like terms: -8.464285714 + 8.464285714 = 0.000000000 0.000000000 + -0.6428571429x + x2 = 0 + 8.464285714 -0.6428571429x + x2 = 0 + 8.464285714 Combine like terms: 0 + 8.464285714 = 8.464285714 -0.6428571429x + x2 = 8.464285714 The x term is -0.6428571429x. Take half its coefficient (-0.3214285715). Square it (0.1033163266) and add it to both sides. Add '0.1033163266' to each side of the equation. -0.6428571429x + 0.1033163266 + x2 = 8.464285714 + 0.1033163266 Reorder the terms: 0.1033163266 + -0.6428571429x + x2 = 8.464285714 + 0.1033163266 Combine like terms: 8.464285714 + 0.1033163266 = 8.5676020406 0.1033163266 + -0.6428571429x + x2 = 8.5676020406 Factor a perfect square on the left side: (x + -0.3214285715)(x + -0.3214285715) = 8.5676020406 Calculate the square root of the right side: 2.927046641 Break this problem into two subproblems by setting (x + -0.3214285715) equal to 2.927046641 and -2.927046641.Subproblem 1
x + -0.3214285715 = 2.927046641 Simplifying x + -0.3214285715 = 2.927046641 Reorder the terms: -0.3214285715 + x = 2.927046641 Solving -0.3214285715 + x = 2.927046641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3214285715' to each side of the equation. -0.3214285715 + 0.3214285715 + x = 2.927046641 + 0.3214285715 Combine like terms: -0.3214285715 + 0.3214285715 = 0.0000000000 0.0000000000 + x = 2.927046641 + 0.3214285715 x = 2.927046641 + 0.3214285715 Combine like terms: 2.927046641 + 0.3214285715 = 3.2484752125 x = 3.2484752125 Simplifying x = 3.2484752125Subproblem 2
x + -0.3214285715 = -2.927046641 Simplifying x + -0.3214285715 = -2.927046641 Reorder the terms: -0.3214285715 + x = -2.927046641 Solving -0.3214285715 + x = -2.927046641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3214285715' to each side of the equation. -0.3214285715 + 0.3214285715 + x = -2.927046641 + 0.3214285715 Combine like terms: -0.3214285715 + 0.3214285715 = 0.0000000000 0.0000000000 + x = -2.927046641 + 0.3214285715 x = -2.927046641 + 0.3214285715 Combine like terms: -2.927046641 + 0.3214285715 = -2.6056180695 x = -2.6056180695 Simplifying x = -2.6056180695Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.2484752125, -2.6056180695}
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