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Simplifying -12x + 5x2 = 75 + 2x Solving -12x + 5x2 = 75 + 2x Solving for variable 'x'. Reorder the terms: -75 + -12x + -2x + 5x2 = 75 + 2x + -75 + -2x Combine like terms: -12x + -2x = -14x -75 + -14x + 5x2 = 75 + 2x + -75 + -2x Reorder the terms: -75 + -14x + 5x2 = 75 + -75 + 2x + -2x Combine like terms: 75 + -75 = 0 -75 + -14x + 5x2 = 0 + 2x + -2x -75 + -14x + 5x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -75 + -14x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -15 + -2.8x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -2.8x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + -2.8x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -2.8x + x2 = 0 + 15 -2.8x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -2.8x + x2 = 15 The x term is -2.8x. Take half its coefficient (-1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. -2.8x + 1.96 + x2 = 15 + 1.96 Reorder the terms: 1.96 + -2.8x + x2 = 15 + 1.96 Combine like terms: 15 + 1.96 = 16.96 1.96 + -2.8x + x2 = 16.96 Factor a perfect square on the left side: (x + -1.4)(x + -1.4) = 16.96 Calculate the square root of the right side: 4.118252056 Break this problem into two subproblems by setting (x + -1.4) equal to 4.118252056 and -4.118252056.Subproblem 1
x + -1.4 = 4.118252056 Simplifying x + -1.4 = 4.118252056 Reorder the terms: -1.4 + x = 4.118252056 Solving -1.4 + x = 4.118252056 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = 4.118252056 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = 4.118252056 + 1.4 x = 4.118252056 + 1.4 Combine like terms: 4.118252056 + 1.4 = 5.518252056 x = 5.518252056 Simplifying x = 5.518252056Subproblem 2
x + -1.4 = -4.118252056 Simplifying x + -1.4 = -4.118252056 Reorder the terms: -1.4 + x = -4.118252056 Solving -1.4 + x = -4.118252056 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = -4.118252056 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = -4.118252056 + 1.4 x = -4.118252056 + 1.4 Combine like terms: -4.118252056 + 1.4 = -2.718252056 x = -2.718252056 Simplifying x = -2.718252056Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.518252056, -2.718252056}
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