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Simplifying 37x2 + -10x + -7 = 0 Reorder the terms: -7 + -10x + 37x2 = 0 Solving -7 + -10x + 37x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 37 the coefficient of the squared term: Divide each side by '37'. -0.1891891892 + -0.2702702703x + x2 = 0 Move the constant term to the right: Add '0.1891891892' to each side of the equation. -0.1891891892 + -0.2702702703x + 0.1891891892 + x2 = 0 + 0.1891891892 Reorder the terms: -0.1891891892 + 0.1891891892 + -0.2702702703x + x2 = 0 + 0.1891891892 Combine like terms: -0.1891891892 + 0.1891891892 = 0.0000000000 0.0000000000 + -0.2702702703x + x2 = 0 + 0.1891891892 -0.2702702703x + x2 = 0 + 0.1891891892 Combine like terms: 0 + 0.1891891892 = 0.1891891892 -0.2702702703x + x2 = 0.1891891892 The x term is -0.2702702703x. Take half its coefficient (-0.1351351352). Square it (0.01826150477) and add it to both sides. Add '0.01826150477' to each side of the equation. -0.2702702703x + 0.01826150477 + x2 = 0.1891891892 + 0.01826150477 Reorder the terms: 0.01826150477 + -0.2702702703x + x2 = 0.1891891892 + 0.01826150477 Combine like terms: 0.1891891892 + 0.01826150477 = 0.20745069397 0.01826150477 + -0.2702702703x + x2 = 0.20745069397 Factor a perfect square on the left side: (x + -0.1351351352)(x + -0.1351351352) = 0.20745069397 Calculate the square root of the right side: 0.455467555 Break this problem into two subproblems by setting (x + -0.1351351352) equal to 0.455467555 and -0.455467555.Subproblem 1
x + -0.1351351352 = 0.455467555 Simplifying x + -0.1351351352 = 0.455467555 Reorder the terms: -0.1351351352 + x = 0.455467555 Solving -0.1351351352 + x = 0.455467555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1351351352' to each side of the equation. -0.1351351352 + 0.1351351352 + x = 0.455467555 + 0.1351351352 Combine like terms: -0.1351351352 + 0.1351351352 = 0.0000000000 0.0000000000 + x = 0.455467555 + 0.1351351352 x = 0.455467555 + 0.1351351352 Combine like terms: 0.455467555 + 0.1351351352 = 0.5906026902 x = 0.5906026902 Simplifying x = 0.5906026902Subproblem 2
x + -0.1351351352 = -0.455467555 Simplifying x + -0.1351351352 = -0.455467555 Reorder the terms: -0.1351351352 + x = -0.455467555 Solving -0.1351351352 + x = -0.455467555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1351351352' to each side of the equation. -0.1351351352 + 0.1351351352 + x = -0.455467555 + 0.1351351352 Combine like terms: -0.1351351352 + 0.1351351352 = 0.0000000000 0.0000000000 + x = -0.455467555 + 0.1351351352 x = -0.455467555 + 0.1351351352 Combine like terms: -0.455467555 + 0.1351351352 = -0.3203324198 x = -0.3203324198 Simplifying x = -0.3203324198Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5906026902, -0.3203324198}
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