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Simplifying 12.67x2 + 31.19x + 8.07 = 0 Reorder the terms: 8.07 + 31.19x + 12.67x2 = 0 Solving 8.07 + 31.19x + 12.67x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12.67 the coefficient of the squared term: Divide each side by '12.67'. 0.636937648 + 2.4617206x + x2 = 0 Move the constant term to the right: Add '-0.636937648' to each side of the equation. 0.636937648 + 2.4617206x + -0.636937648 + x2 = 0 + -0.636937648 Reorder the terms: 0.636937648 + -0.636937648 + 2.4617206x + x2 = 0 + -0.636937648 Combine like terms: 0.636937648 + -0.636937648 = 0.000000000 0.000000000 + 2.4617206x + x2 = 0 + -0.636937648 2.4617206x + x2 = 0 + -0.636937648 Combine like terms: 0 + -0.636937648 = -0.636937648 2.4617206x + x2 = -0.636937648 The x term is 2.4617206x. Take half its coefficient (1.2308603). Square it (1.515017078) and add it to both sides. Add '1.515017078' to each side of the equation. 2.4617206x + 1.515017078 + x2 = -0.636937648 + 1.515017078 Reorder the terms: 1.515017078 + 2.4617206x + x2 = -0.636937648 + 1.515017078 Combine like terms: -0.636937648 + 1.515017078 = 0.87807943 1.515017078 + 2.4617206x + x2 = 0.87807943 Factor a perfect square on the left side: (x + 1.2308603)(x + 1.2308603) = 0.87807943 Calculate the square root of the right side: 0.937058926 Break this problem into two subproblems by setting (x + 1.2308603) equal to 0.937058926 and -0.937058926.Subproblem 1
x + 1.2308603 = 0.937058926 Simplifying x + 1.2308603 = 0.937058926 Reorder the terms: 1.2308603 + x = 0.937058926 Solving 1.2308603 + x = 0.937058926 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2308603' to each side of the equation. 1.2308603 + -1.2308603 + x = 0.937058926 + -1.2308603 Combine like terms: 1.2308603 + -1.2308603 = 0.0000000 0.0000000 + x = 0.937058926 + -1.2308603 x = 0.937058926 + -1.2308603 Combine like terms: 0.937058926 + -1.2308603 = -0.293801374 x = -0.293801374 Simplifying x = -0.293801374Subproblem 2
x + 1.2308603 = -0.937058926 Simplifying x + 1.2308603 = -0.937058926 Reorder the terms: 1.2308603 + x = -0.937058926 Solving 1.2308603 + x = -0.937058926 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2308603' to each side of the equation. 1.2308603 + -1.2308603 + x = -0.937058926 + -1.2308603 Combine like terms: 1.2308603 + -1.2308603 = 0.0000000 0.0000000 + x = -0.937058926 + -1.2308603 x = -0.937058926 + -1.2308603 Combine like terms: -0.937058926 + -1.2308603 = -2.167919226 x = -2.167919226 Simplifying x = -2.167919226Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.293801374, -2.167919226}
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