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Simplifying 375x2 + -15x + -2 = 0 Reorder the terms: -2 + -15x + 375x2 = 0 Solving -2 + -15x + 375x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 375 the coefficient of the squared term: Divide each side by '375'. -0.005333333333 + -0.04x + x2 = 0 Move the constant term to the right: Add '0.005333333333' to each side of the equation. -0.005333333333 + -0.04x + 0.005333333333 + x2 = 0 + 0.005333333333 Reorder the terms: -0.005333333333 + 0.005333333333 + -0.04x + x2 = 0 + 0.005333333333 Combine like terms: -0.005333333333 + 0.005333333333 = 0.000000000000 0.000000000000 + -0.04x + x2 = 0 + 0.005333333333 -0.04x + x2 = 0 + 0.005333333333 Combine like terms: 0 + 0.005333333333 = 0.005333333333 -0.04x + x2 = 0.005333333333 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 = 0.005333333333 + 0.0004 Reorder the terms: 0.0004 + -0.04x + x2 = 0.005333333333 + 0.0004 Combine like terms: 0.005333333333 + 0.0004 = 0.005733333333 0.0004 + -0.04x + x2 = 0.005733333333 Factor a perfect square on the left side: (x + -0.02)(x + -0.02) = 0.005733333333 Calculate the square root of the right side: 0.075718778 Break this problem into two subproblems by setting (x + -0.02) equal to 0.075718778 and -0.075718778.Subproblem 1
x + -0.02 = 0.075718778 Simplifying x + -0.02 = 0.075718778 Reorder the terms: -0.02 + x = 0.075718778 Solving -0.02 + x = 0.075718778 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 = 0.075718778 + 0.02 Combine like terms: -0.02 + 0.02 = 0.00 0.00 + x = 0.075718778 + 0.02 x = 0.075718778 + 0.02 Combine like terms: 0.075718778 + 0.02 = 0.095718778 x = 0.095718778 Simplifying x = 0.095718778Subproblem 2
x + -0.02 = -0.075718778 Simplifying x + -0.02 = -0.075718778 Reorder the terms: -0.02 + x = -0.075718778 Solving -0.02 + x = -0.075718778 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 = -0.075718778 + 0.02 Combine like terms: -0.02 + 0.02 = 0.00 0.00 + x = -0.075718778 + 0.02 x = -0.075718778 + 0.02 Combine like terms: -0.075718778 + 0.02 = -0.055718778 x = -0.055718778 Simplifying x = -0.055718778Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.095718778, -0.055718778}
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