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Simplifying 0.04x2 + -1.029x + 0.005 = 0 Reorder the terms: 0.005 + -1.029x + 0.04x2 = 0 Solving 0.005 + -1.029x + 0.04x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.04 the coefficient of the squared term: Divide each side by '0.04'. 0.125 + -25.725x + x2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + -25.725x + -0.125 + x2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + -25.725x + x2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + -25.725x + x2 = 0 + -0.125 -25.725x + x2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 -25.725x + x2 = -0.125 The x term is -25.725x. Take half its coefficient (-12.8625). Square it (165.4439063) and add it to both sides. Add '165.4439063' to each side of the equation. -25.725x + 165.4439063 + x2 = -0.125 + 165.4439063 Reorder the terms: 165.4439063 + -25.725x + x2 = -0.125 + 165.4439063 Combine like terms: -0.125 + 165.4439063 = 165.3189063 165.4439063 + -25.725x + x2 = 165.3189063 Factor a perfect square on the left side: (x + -12.8625)(x + -12.8625) = 165.3189063 Calculate the square root of the right side: 12.857639997 Break this problem into two subproblems by setting (x + -12.8625) equal to 12.857639997 and -12.857639997.Subproblem 1
x + -12.8625 = 12.857639997 Simplifying x + -12.8625 = 12.857639997 Reorder the terms: -12.8625 + x = 12.857639997 Solving -12.8625 + x = 12.857639997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.8625' to each side of the equation. -12.8625 + 12.8625 + x = 12.857639997 + 12.8625 Combine like terms: -12.8625 + 12.8625 = 0.0000 0.0000 + x = 12.857639997 + 12.8625 x = 12.857639997 + 12.8625 Combine like terms: 12.857639997 + 12.8625 = 25.720139997 x = 25.720139997 Simplifying x = 25.720139997Subproblem 2
x + -12.8625 = -12.857639997 Simplifying x + -12.8625 = -12.857639997 Reorder the terms: -12.8625 + x = -12.857639997 Solving -12.8625 + x = -12.857639997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.8625' to each side of the equation. -12.8625 + 12.8625 + x = -12.857639997 + 12.8625 Combine like terms: -12.8625 + 12.8625 = 0.0000 0.0000 + x = -12.857639997 + 12.8625 x = -12.857639997 + 12.8625 Combine like terms: -12.857639997 + 12.8625 = 0.004860003 x = 0.004860003 Simplifying x = 0.004860003Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.720139997, 0.004860003}
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