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Simplifying x2 + 7x + -10 = 5 Reorder the terms: -10 + 7x + x2 = 5 Solving -10 + 7x + x2 = 5 Solving for variable 'x'. Reorder the terms: -10 + -5 + 7x + x2 = 5 + -5 Combine like terms: -10 + -5 = -15 -15 + 7x + x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -15 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 7x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 7x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 7x + x2 = 0 + 15 7x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 7x + x2 = 15 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 = 15 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 15 + 12.25 Combine like terms: 15 + 12.25 = 27.25 12.25 + 7x + x2 = 27.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (x + 3.5) equal to 5.220153254 and -5.220153254.Subproblem 1
x + 3.5 = 5.220153254 Simplifying x + 3.5 = 5.220153254 Reorder the terms: 3.5 + x = 5.220153254 Solving 3.5 + x = 5.220153254 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 = 5.220153254 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 5.220153254 + -3.5 x = 5.220153254 + -3.5 Combine like terms: 5.220153254 + -3.5 = 1.720153254 x = 1.720153254 Simplifying x = 1.720153254Subproblem 2
x + 3.5 = -5.220153254 Simplifying x + 3.5 = -5.220153254 Reorder the terms: 3.5 + x = -5.220153254 Solving 3.5 + x = -5.220153254 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 = -5.220153254 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -5.220153254 + -3.5 x = -5.220153254 + -3.5 Combine like terms: -5.220153254 + -3.5 = -8.720153254 x = -8.720153254 Simplifying x = -8.720153254Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.720153254, -8.720153254}
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