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Simplifying 2x2 + -32x = 19 Reorder the terms: -32x + 2x2 = 19 Solving -32x + 2x2 = 19 Solving for variable 'x'. Reorder the terms: -19 + -32x + 2x2 = 19 + -19 Combine like terms: 19 + -19 = 0 -19 + -32x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -9.5 + -16x + x2 = 0 Move the constant term to the right: Add '9.5' to each side of the equation. -9.5 + -16x + 9.5 + x2 = 0 + 9.5 Reorder the terms: -9.5 + 9.5 + -16x + x2 = 0 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + -16x + x2 = 0 + 9.5 -16x + x2 = 0 + 9.5 Combine like terms: 0 + 9.5 = 9.5 -16x + x2 = 9.5 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = 9.5 + 64 Reorder the terms: 64 + -16x + x2 = 9.5 + 64 Combine like terms: 9.5 + 64 = 73.5 64 + -16x + x2 = 73.5 Factor a perfect square on the left side: (x + -8)(x + -8) = 73.5 Calculate the square root of the right side: 8.5732141 Break this problem into two subproblems by setting (x + -8) equal to 8.5732141 and -8.5732141.Subproblem 1
x + -8 = 8.5732141 Simplifying x + -8 = 8.5732141 Reorder the terms: -8 + x = 8.5732141 Solving -8 + x = 8.5732141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 8.5732141 + 8 Combine like terms: -8 + 8 = 0 0 + x = 8.5732141 + 8 x = 8.5732141 + 8 Combine like terms: 8.5732141 + 8 = 16.5732141 x = 16.5732141 Simplifying x = 16.5732141Subproblem 2
x + -8 = -8.5732141 Simplifying x + -8 = -8.5732141 Reorder the terms: -8 + x = -8.5732141 Solving -8 + x = -8.5732141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -8.5732141 + 8 Combine like terms: -8 + 8 = 0 0 + x = -8.5732141 + 8 x = -8.5732141 + 8 Combine like terms: -8.5732141 + 8 = -0.5732141 x = -0.5732141 Simplifying x = -0.5732141Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.5732141, -0.5732141}
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