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Simplifying -10x2 + 10(-5x2) + (-3x) + 7 = 0 Remove parenthesis around (-5x2) -10x2 + 10 * -5x2 + (-3x) + 7 = 0 Multiply 10 * -5 -10x2 + -50x2 + (-3x) + 7 = 0 Reorder the terms: 7 + (-3x) + -10x2 + -50x2 = 0 Combine like terms: -10x2 + -50x2 = -60x2 7 + (-3x) + -60x2 = 0 Solving 7 + (-3x) + -60x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -60 the coefficient of the squared term: Divide each side by '-60'. -0.1166666667 + (0.05x) + x2 = 0.0 Move the constant term to the right: Add '0.1166666667' to each side of the equation. -0.1166666667 + (0.05x) + 0.1166666667 + x2 = 0.0 + 0.1166666667 Reorder the terms: -0.1166666667 + 0.1166666667 + (0.05x) + x2 = 0.0 + 0.1166666667 Combine like terms: -0.1166666667 + 0.1166666667 = 0.0000000000 0.0000000000 + (0.05x) + x2 = 0.0 + 0.1166666667 (0.05x) + x2 = 0.0 + 0.1166666667 Combine like terms: 0.0 + 0.1166666667 = 0.1166666667 (0.05x) + x2 = 0.1166666667 The x term is (0.05x). Take half its coefficient (0.025). Square it (0.000625) and add it to both sides. Add '0.000625' to each side of the equation. (0.05x) + 0.000625 + x2 = 0.1166666667 + 0.000625 Reorder the terms: 0.000625 + (0.05x) + x2 = 0.1166666667 + 0.000625 Combine like terms: 0.1166666667 + 0.000625 = 0.1172916667 0.000625 + (0.05x) + x2 = 0.1172916667 Factor a perfect square on the left side: (x + 0.025)(x + 0.025) = 0.1172916667 Calculate the square root of the right side: 0.34247871 Break this problem into two subproblems by setting (x + 0.025) equal to 0.34247871 and -0.34247871.Subproblem 1
x + 0.025 = 0.34247871 Simplifying x + 0.025 = 0.34247871 Reorder the terms: 0.025 + x = 0.34247871 Solving 0.025 + x = 0.34247871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.025' to each side of the equation. 0.025 + -0.025 + x = 0.34247871 + -0.025 Combine like terms: 0.025 + -0.025 = 0.000 0.000 + x = 0.34247871 + -0.025 x = 0.34247871 + -0.025 Combine like terms: 0.34247871 + -0.025 = 0.31747871 x = 0.31747871 Simplifying x = 0.31747871Subproblem 2
x + 0.025 = -0.34247871 Simplifying x + 0.025 = -0.34247871 Reorder the terms: 0.025 + x = -0.34247871 Solving 0.025 + x = -0.34247871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.025' to each side of the equation. 0.025 + -0.025 + x = -0.34247871 + -0.025 Combine like terms: 0.025 + -0.025 = 0.000 0.000 + x = -0.34247871 + -0.025 x = -0.34247871 + -0.025 Combine like terms: -0.34247871 + -0.025 = -0.36747871 x = -0.36747871 Simplifying x = -0.36747871Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.31747871, -0.36747871}
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