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Simplifying -10x2 + -7x + -9 = -17 Reorder the terms: -9 + -7x + -10x2 = -17 Solving -9 + -7x + -10x2 = -17 Solving for variable 'x'. Reorder the terms: -9 + 17 + -7x + -10x2 = -17 + 17 Combine like terms: -9 + 17 = 8 8 + -7x + -10x2 = -17 + 17 Combine like terms: -17 + 17 = 0 8 + -7x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -0.8 + 0.7x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 0.7x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + 0.7x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 0.7x + x2 = 0 + 0.8 0.7x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 0.7x + x2 = 0.8 The x term is 0.7x. Take half its coefficient (0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. 0.7x + 0.1225 + x2 = 0.8 + 0.1225 Reorder the terms: 0.1225 + 0.7x + x2 = 0.8 + 0.1225 Combine like terms: 0.8 + 0.1225 = 0.9225 0.1225 + 0.7x + x2 = 0.9225 Factor a perfect square on the left side: (x + 0.35)(x + 0.35) = 0.9225 Calculate the square root of the right side: 0.960468636 Break this problem into two subproblems by setting (x + 0.35) equal to 0.960468636 and -0.960468636.Subproblem 1
x + 0.35 = 0.960468636 Simplifying x + 0.35 = 0.960468636 Reorder the terms: 0.35 + x = 0.960468636 Solving 0.35 + x = 0.960468636 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + x = 0.960468636 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + x = 0.960468636 + -0.35 x = 0.960468636 + -0.35 Combine like terms: 0.960468636 + -0.35 = 0.610468636 x = 0.610468636 Simplifying x = 0.610468636Subproblem 2
x + 0.35 = -0.960468636 Simplifying x + 0.35 = -0.960468636 Reorder the terms: 0.35 + x = -0.960468636 Solving 0.35 + x = -0.960468636 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + x = -0.960468636 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + x = -0.960468636 + -0.35 x = -0.960468636 + -0.35 Combine like terms: -0.960468636 + -0.35 = -1.310468636 x = -1.310468636 Simplifying x = -1.310468636Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.610468636, -1.310468636}
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