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Simplifying (10x2 + -23x + -12) = 0 Reorder the terms: (-12 + -23x + 10x2) = 0 Remove parenthesis around (-12 + -23x + 10x2) -12 + -23x + 10x2 = 0 Solving -12 + -23x + 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'. -1.2 + -2.3x + x2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -2.3x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + -2.3x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -2.3x + x2 = 0 + 1.2 -2.3x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 -2.3x + x2 = 1.2 The x term is -2.3x. Take half its coefficient (-1.15). Square it (1.3225) and add it to both sides. Add '1.3225' to each side of the equation. -2.3x + 1.3225 + x2 = 1.2 + 1.3225 Reorder the terms: 1.3225 + -2.3x + x2 = 1.2 + 1.3225 Combine like terms: 1.2 + 1.3225 = 2.5225 1.3225 + -2.3x + x2 = 2.5225 Factor a perfect square on the left side: (x + -1.15)(x + -1.15) = 2.5225 Calculate the square root of the right side: 1.588238017 Break this problem into two subproblems by setting (x + -1.15) equal to 1.588238017 and -1.588238017.Subproblem 1
x + -1.15 = 1.588238017 Simplifying x + -1.15 = 1.588238017 Reorder the terms: -1.15 + x = 1.588238017 Solving -1.15 + x = 1.588238017 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.15' to each side of the equation. -1.15 + 1.15 + x = 1.588238017 + 1.15 Combine like terms: -1.15 + 1.15 = 0.00 0.00 + x = 1.588238017 + 1.15 x = 1.588238017 + 1.15 Combine like terms: 1.588238017 + 1.15 = 2.738238017 x = 2.738238017 Simplifying x = 2.738238017Subproblem 2
x + -1.15 = -1.588238017 Simplifying x + -1.15 = -1.588238017 Reorder the terms: -1.15 + x = -1.588238017 Solving -1.15 + x = -1.588238017 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.15' to each side of the equation. -1.15 + 1.15 + x = -1.588238017 + 1.15 Combine like terms: -1.15 + 1.15 = 0.00 0.00 + x = -1.588238017 + 1.15 x = -1.588238017 + 1.15 Combine like terms: -1.588238017 + 1.15 = -0.438238017 x = -0.438238017 Simplifying x = -0.438238017Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.738238017, -0.438238017}
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