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Simplifying x(2x + -7) = 192 Reorder the terms: x(-7 + 2x) = 192 (-7 * x + 2x * x) = 192 (-7x + 2x2) = 192 Solving -7x + 2x2 = 192 Solving for variable 'x'. Reorder the terms: -192 + -7x + 2x2 = 192 + -192 Combine like terms: 192 + -192 = 0 -192 + -7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -96 + -3.5x + x2 = 0 Move the constant term to the right: Add '96' to each side of the equation. -96 + -3.5x + 96 + x2 = 0 + 96 Reorder the terms: -96 + 96 + -3.5x + x2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + -3.5x + x2 = 0 + 96 -3.5x + x2 = 0 + 96 Combine like terms: 0 + 96 = 96 -3.5x + x2 = 96 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 96 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 96 + 3.0625 Combine like terms: 96 + 3.0625 = 99.0625 3.0625 + -3.5x + x2 = 99.0625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 99.0625 Calculate the square root of the right side: 9.953014619 Break this problem into two subproblems by setting (x + -1.75) equal to 9.953014619 and -9.953014619.Subproblem 1
x + -1.75 = 9.953014619 Simplifying x + -1.75 = 9.953014619 Reorder the terms: -1.75 + x = 9.953014619 Solving -1.75 + x = 9.953014619 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 9.953014619 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 9.953014619 + 1.75 x = 9.953014619 + 1.75 Combine like terms: 9.953014619 + 1.75 = 11.703014619 x = 11.703014619 Simplifying x = 11.703014619Subproblem 2
x + -1.75 = -9.953014619 Simplifying x + -1.75 = -9.953014619 Reorder the terms: -1.75 + x = -9.953014619 Solving -1.75 + x = -9.953014619 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -9.953014619 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -9.953014619 + 1.75 x = -9.953014619 + 1.75 Combine like terms: -9.953014619 + 1.75 = -8.203014619 x = -8.203014619 Simplifying x = -8.203014619Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.703014619, -8.203014619}
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