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Simplifying 151x2 + 7x + -18 = 0 Reorder the terms: -18 + 7x + 151x2 = 0 Solving -18 + 7x + 151x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 151 the coefficient of the squared term: Divide each side by '151'. -0.119205298 + 0.04635761589x + x2 = 0 Move the constant term to the right: Add '0.119205298' to each side of the equation. -0.119205298 + 0.04635761589x + 0.119205298 + x2 = 0 + 0.119205298 Reorder the terms: -0.119205298 + 0.119205298 + 0.04635761589x + x2 = 0 + 0.119205298 Combine like terms: -0.119205298 + 0.119205298 = 0.000000000 0.000000000 + 0.04635761589x + x2 = 0 + 0.119205298 0.04635761589x + x2 = 0 + 0.119205298 Combine like terms: 0 + 0.119205298 = 0.119205298 0.04635761589x + x2 = 0.119205298 The x term is 0.04635761589x. Take half its coefficient (0.02317880795). Square it (0.0005372571380) and add it to both sides. Add '0.0005372571380' to each side of the equation. 0.04635761589x + 0.0005372571380 + x2 = 0.119205298 + 0.0005372571380 Reorder the terms: 0.0005372571380 + 0.04635761589x + x2 = 0.119205298 + 0.0005372571380 Combine like terms: 0.119205298 + 0.0005372571380 = 0.119742555138 0.0005372571380 + 0.04635761589x + x2 = 0.119742555138 Factor a perfect square on the left side: (x + 0.02317880795)(x + 0.02317880795) = 0.119742555138 Calculate the square root of the right side: 0.346038372 Break this problem into two subproblems by setting (x + 0.02317880795) equal to 0.346038372 and -0.346038372.Subproblem 1
x + 0.02317880795 = 0.346038372 Simplifying x + 0.02317880795 = 0.346038372 Reorder the terms: 0.02317880795 + x = 0.346038372 Solving 0.02317880795 + x = 0.346038372 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02317880795' to each side of the equation. 0.02317880795 + -0.02317880795 + x = 0.346038372 + -0.02317880795 Combine like terms: 0.02317880795 + -0.02317880795 = 0.00000000000 0.00000000000 + x = 0.346038372 + -0.02317880795 x = 0.346038372 + -0.02317880795 Combine like terms: 0.346038372 + -0.02317880795 = 0.32285956405 x = 0.32285956405 Simplifying x = 0.32285956405Subproblem 2
x + 0.02317880795 = -0.346038372 Simplifying x + 0.02317880795 = -0.346038372 Reorder the terms: 0.02317880795 + x = -0.346038372 Solving 0.02317880795 + x = -0.346038372 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02317880795' to each side of the equation. 0.02317880795 + -0.02317880795 + x = -0.346038372 + -0.02317880795 Combine like terms: 0.02317880795 + -0.02317880795 = 0.00000000000 0.00000000000 + x = -0.346038372 + -0.02317880795 x = -0.346038372 + -0.02317880795 Combine like terms: -0.346038372 + -0.02317880795 = -0.36921717995 x = -0.36921717995 Simplifying x = -0.36921717995Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.32285956405, -0.36921717995}
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