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Simplifying 10x2 + -7x + -24 = 0 Reorder the terms: -24 + -7x + 10x2 = 0 Solving -24 + -7x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -2.4 + -0.7x + x2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + -0.7x + 2.4 + x2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + -0.7x + x2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + -0.7x + x2 = 0 + 2.4 -0.7x + x2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 -0.7x + x2 = 2.4 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 = 2.4 + 0.1225 Reorder the terms: 0.1225 + -0.7x + x2 = 2.4 + 0.1225 Combine like terms: 2.4 + 0.1225 = 2.5225 0.1225 + -0.7x + x2 = 2.5225 Factor a perfect square on the left side: (x + -0.35)(x + -0.35) = 2.5225 Calculate the square root of the right side: 1.588238017 Break this problem into two subproblems by setting (x + -0.35) equal to 1.588238017 and -1.588238017.Subproblem 1
x + -0.35 = 1.588238017 Simplifying x + -0.35 = 1.588238017 Reorder the terms: -0.35 + x = 1.588238017 Solving -0.35 + x = 1.588238017 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 = 1.588238017 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + x = 1.588238017 + 0.35 x = 1.588238017 + 0.35 Combine like terms: 1.588238017 + 0.35 = 1.938238017 x = 1.938238017 Simplifying x = 1.938238017Subproblem 2
x + -0.35 = -1.588238017 Simplifying x + -0.35 = -1.588238017 Reorder the terms: -0.35 + x = -1.588238017 Solving -0.35 + x = -1.588238017 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 = -1.588238017 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + x = -1.588238017 + 0.35 x = -1.588238017 + 0.35 Combine like terms: -1.588238017 + 0.35 = -1.238238017 x = -1.238238017 Simplifying x = -1.238238017Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.938238017, -1.238238017}
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