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Simplifying x(x + -7) = 458 Reorder the terms: x(-7 + x) = 458 (-7 * x + x * x) = 458 (-7x + x2) = 458 Solving -7x + x2 = 458 Solving for variable 'x'. Reorder the terms: -458 + -7x + x2 = 458 + -458 Combine like terms: 458 + -458 = 0 -458 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '458' to each side of the equation. -458 + -7x + 458 + x2 = 0 + 458 Reorder the terms: -458 + 458 + -7x + x2 = 0 + 458 Combine like terms: -458 + 458 = 0 0 + -7x + x2 = 0 + 458 -7x + x2 = 0 + 458 Combine like terms: 0 + 458 = 458 -7x + x2 = 458 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 458 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 458 + 12.25 Combine like terms: 458 + 12.25 = 470.25 12.25 + -7x + x2 = 470.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 470.25 Calculate the square root of the right side: 21.685248442 Break this problem into two subproblems by setting (x + -3.5) equal to 21.685248442 and -21.685248442.Subproblem 1
x + -3.5 = 21.685248442 Simplifying x + -3.5 = 21.685248442 Reorder the terms: -3.5 + x = 21.685248442 Solving -3.5 + x = 21.685248442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 21.685248442 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 21.685248442 + 3.5 x = 21.685248442 + 3.5 Combine like terms: 21.685248442 + 3.5 = 25.185248442 x = 25.185248442 Simplifying x = 25.185248442Subproblem 2
x + -3.5 = -21.685248442 Simplifying x + -3.5 = -21.685248442 Reorder the terms: -3.5 + x = -21.685248442 Solving -3.5 + x = -21.685248442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -21.685248442 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -21.685248442 + 3.5 x = -21.685248442 + 3.5 Combine like terms: -21.685248442 + 3.5 = -18.185248442 x = -18.185248442 Simplifying x = -18.185248442Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.185248442, -18.185248442}
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