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Simplifying 50x2 + -2x + -67 = 0 Reorder the terms: -67 + -2x + 50x2 = 0 Solving -67 + -2x + 50x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 50 the coefficient of the squared term: Divide each side by '50'. -1.34 + -0.04x + x2 = 0 Move the constant term to the right: Add '1.34' to each side of the equation. -1.34 + -0.04x + 1.34 + x2 = 0 + 1.34 Reorder the terms: -1.34 + 1.34 + -0.04x + x2 = 0 + 1.34 Combine like terms: -1.34 + 1.34 = 0.00 0.00 + -0.04x + x2 = 0 + 1.34 -0.04x + x2 = 0 + 1.34 Combine like terms: 0 + 1.34 = 1.34 -0.04x + x2 = 1.34 The x term is -0.04x. Take half its coefficient (-0.02). Square it (0.0004) and add it to both sides. Add '0.0004' to each side of the equation. -0.04x + 0.0004 + x2 = 1.34 + 0.0004 Reorder the terms: 0.0004 + -0.04x + x2 = 1.34 + 0.0004 Combine like terms: 1.34 + 0.0004 = 1.3404 0.0004 + -0.04x + x2 = 1.3404 Factor a perfect square on the left side: (x + -0.02)(x + -0.02) = 1.3404 Calculate the square root of the right side: 1.157756451 Break this problem into two subproblems by setting (x + -0.02) equal to 1.157756451 and -1.157756451.Subproblem 1
x + -0.02 = 1.157756451 Simplifying x + -0.02 = 1.157756451 Reorder the terms: -0.02 + x = 1.157756451 Solving -0.02 + x = 1.157756451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02' to each side of the equation. -0.02 + 0.02 + x = 1.157756451 + 0.02 Combine like terms: -0.02 + 0.02 = 0.00 0.00 + x = 1.157756451 + 0.02 x = 1.157756451 + 0.02 Combine like terms: 1.157756451 + 0.02 = 1.177756451 x = 1.177756451 Simplifying x = 1.177756451Subproblem 2
x + -0.02 = -1.157756451 Simplifying x + -0.02 = -1.157756451 Reorder the terms: -0.02 + x = -1.157756451 Solving -0.02 + x = -1.157756451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02' to each side of the equation. -0.02 + 0.02 + x = -1.157756451 + 0.02 Combine like terms: -0.02 + 0.02 = 0.00 0.00 + x = -1.157756451 + 0.02 x = -1.157756451 + 0.02 Combine like terms: -1.157756451 + 0.02 = -1.137756451 x = -1.137756451 Simplifying x = -1.137756451Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.177756451, -1.137756451}
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