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Simplifying 5x2 + -14x + -76 = 0 Reorder the terms: -76 + -14x + 5x2 = 0 Solving -76 + -14x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -15.2 + -2.8x + x2 = 0 Move the constant term to the right: Add '15.2' to each side of the equation. -15.2 + -2.8x + 15.2 + x2 = 0 + 15.2 Reorder the terms: -15.2 + 15.2 + -2.8x + x2 = 0 + 15.2 Combine like terms: -15.2 + 15.2 = 0.0 0.0 + -2.8x + x2 = 0 + 15.2 -2.8x + x2 = 0 + 15.2 Combine like terms: 0 + 15.2 = 15.2 -2.8x + x2 = 15.2 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 = 15.2 + 1.96 Reorder the terms: 1.96 + -2.8x + x2 = 15.2 + 1.96 Combine like terms: 15.2 + 1.96 = 17.16 1.96 + -2.8x + x2 = 17.16 Factor a perfect square on the left side: (x + -1.4)(x + -1.4) = 17.16 Calculate the square root of the right side: 4.142463035 Break this problem into two subproblems by setting (x + -1.4) equal to 4.142463035 and -4.142463035.Subproblem 1
x + -1.4 = 4.142463035 Simplifying x + -1.4 = 4.142463035 Reorder the terms: -1.4 + x = 4.142463035 Solving -1.4 + x = 4.142463035 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 = 4.142463035 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = 4.142463035 + 1.4 x = 4.142463035 + 1.4 Combine like terms: 4.142463035 + 1.4 = 5.542463035 x = 5.542463035 Simplifying x = 5.542463035Subproblem 2
x + -1.4 = -4.142463035 Simplifying x + -1.4 = -4.142463035 Reorder the terms: -1.4 + x = -4.142463035 Solving -1.4 + x = -4.142463035 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 = -4.142463035 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = -4.142463035 + 1.4 x = -4.142463035 + 1.4 Combine like terms: -4.142463035 + 1.4 = -2.742463035 x = -2.742463035 Simplifying x = -2.742463035Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.542463035, -2.742463035}
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