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Simplifying 5x2 + -10x + -25 = 47 Reorder the terms: -25 + -10x + 5x2 = 47 Solving -25 + -10x + 5x2 = 47 Solving for variable 'x'. Reorder the terms: -25 + -47 + -10x + 5x2 = 47 + -47 Combine like terms: -25 + -47 = -72 -72 + -10x + 5x2 = 47 + -47 Combine like terms: 47 + -47 = 0 -72 + -10x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -14.4 + -2x + x2 = 0 Move the constant term to the right: Add '14.4' to each side of the equation. -14.4 + -2x + 14.4 + x2 = 0 + 14.4 Reorder the terms: -14.4 + 14.4 + -2x + x2 = 0 + 14.4 Combine like terms: -14.4 + 14.4 = 0.0 0.0 + -2x + x2 = 0 + 14.4 -2x + x2 = 0 + 14.4 Combine like terms: 0 + 14.4 = 14.4 -2x + x2 = 14.4 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 14.4 + 1 Reorder the terms: 1 + -2x + x2 = 14.4 + 1 Combine like terms: 14.4 + 1 = 15.4 1 + -2x + x2 = 15.4 Factor a perfect square on the left side: (x + -1)(x + -1) = 15.4 Calculate the square root of the right side: 3.924283374 Break this problem into two subproblems by setting (x + -1) equal to 3.924283374 and -3.924283374.Subproblem 1
x + -1 = 3.924283374 Simplifying x + -1 = 3.924283374 Reorder the terms: -1 + x = 3.924283374 Solving -1 + x = 3.924283374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 3.924283374 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.924283374 + 1 x = 3.924283374 + 1 Combine like terms: 3.924283374 + 1 = 4.924283374 x = 4.924283374 Simplifying x = 4.924283374Subproblem 2
x + -1 = -3.924283374 Simplifying x + -1 = -3.924283374 Reorder the terms: -1 + x = -3.924283374 Solving -1 + x = -3.924283374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -3.924283374 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.924283374 + 1 x = -3.924283374 + 1 Combine like terms: -3.924283374 + 1 = -2.924283374 x = -2.924283374 Simplifying x = -2.924283374Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.924283374, -2.924283374}
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