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Simplifying 0 = 10x2 + 32x + 3.7 Reorder the terms: 0 = 3.7 + 32x + 10x2 Solving 0 = 3.7 + 32x + 10x2 Solving for variable 'x'. Combine like terms: 0 + -3.7 = -3.7 -3.7 + -32x + -10x2 = 3.7 + 32x + 10x2 + -3.7 + -32x + -10x2 Reorder the terms: -3.7 + -32x + -10x2 = 3.7 + -3.7 + 32x + -32x + 10x2 + -10x2 Combine like terms: 3.7 + -3.7 = 0.0 -3.7 + -32x + -10x2 = 0.0 + 32x + -32x + 10x2 + -10x2 -3.7 + -32x + -10x2 = 32x + -32x + 10x2 + -10x2 Combine like terms: 32x + -32x = 0 -3.7 + -32x + -10x2 = 0 + 10x2 + -10x2 -3.7 + -32x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 -3.7 + -32x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. 0.37 + 3.2x + x2 = 0 Move the constant term to the right: Add '-0.37' to each side of the equation. 0.37 + 3.2x + -0.37 + x2 = 0 + -0.37 Reorder the terms: 0.37 + -0.37 + 3.2x + x2 = 0 + -0.37 Combine like terms: 0.37 + -0.37 = 0.00 0.00 + 3.2x + x2 = 0 + -0.37 3.2x + x2 = 0 + -0.37 Combine like terms: 0 + -0.37 = -0.37 3.2x + x2 = -0.37 The x term is 3.2x. Take half its coefficient (1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. 3.2x + 2.56 + x2 = -0.37 + 2.56 Reorder the terms: 2.56 + 3.2x + x2 = -0.37 + 2.56 Combine like terms: -0.37 + 2.56 = 2.19 2.56 + 3.2x + x2 = 2.19 Factor a perfect square on the left side: (x + 1.6)(x + 1.6) = 2.19 Calculate the square root of the right side: 1.479864859 Break this problem into two subproblems by setting (x + 1.6) equal to 1.479864859 and -1.479864859.Subproblem 1
x + 1.6 = 1.479864859 Simplifying x + 1.6 = 1.479864859 Reorder the terms: 1.6 + x = 1.479864859 Solving 1.6 + x = 1.479864859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = 1.479864859 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = 1.479864859 + -1.6 x = 1.479864859 + -1.6 Combine like terms: 1.479864859 + -1.6 = -0.120135141 x = -0.120135141 Simplifying x = -0.120135141Subproblem 2
x + 1.6 = -1.479864859 Simplifying x + 1.6 = -1.479864859 Reorder the terms: 1.6 + x = -1.479864859 Solving 1.6 + x = -1.479864859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = -1.479864859 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = -1.479864859 + -1.6 x = -1.479864859 + -1.6 Combine like terms: -1.479864859 + -1.6 = -3.079864859 x = -3.079864859 Simplifying x = -3.079864859Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.120135141, -3.079864859}
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