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Simplifying 40x2 + -12x + -3 = 0 Reorder the terms: -3 + -12x + 40x2 = 0 Solving -3 + -12x + 40x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. -0.075 + -0.3x + x2 = 0 Move the constant term to the right: Add '0.075' to each side of the equation. -0.075 + -0.3x + 0.075 + x2 = 0 + 0.075 Reorder the terms: -0.075 + 0.075 + -0.3x + x2 = 0 + 0.075 Combine like terms: -0.075 + 0.075 = 0.000 0.000 + -0.3x + x2 = 0 + 0.075 -0.3x + x2 = 0 + 0.075 Combine like terms: 0 + 0.075 = 0.075 -0.3x + x2 = 0.075 The x term is -0.3x. Take half its coefficient (-0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. -0.3x + 0.0225 + x2 = 0.075 + 0.0225 Reorder the terms: 0.0225 + -0.3x + x2 = 0.075 + 0.0225 Combine like terms: 0.075 + 0.0225 = 0.0975 0.0225 + -0.3x + x2 = 0.0975 Factor a perfect square on the left side: (x + -0.15)(x + -0.15) = 0.0975 Calculate the square root of the right side: 0.3122499 Break this problem into two subproblems by setting (x + -0.15) equal to 0.3122499 and -0.3122499.Subproblem 1
x + -0.15 = 0.3122499 Simplifying x + -0.15 = 0.3122499 Reorder the terms: -0.15 + x = 0.3122499 Solving -0.15 + x = 0.3122499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = 0.3122499 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = 0.3122499 + 0.15 x = 0.3122499 + 0.15 Combine like terms: 0.3122499 + 0.15 = 0.4622499 x = 0.4622499 Simplifying x = 0.4622499Subproblem 2
x + -0.15 = -0.3122499 Simplifying x + -0.15 = -0.3122499 Reorder the terms: -0.15 + x = -0.3122499 Solving -0.15 + x = -0.3122499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = -0.3122499 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = -0.3122499 + 0.15 x = -0.3122499 + 0.15 Combine like terms: -0.3122499 + 0.15 = -0.1622499 x = -0.1622499 Simplifying x = -0.1622499Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4622499, -0.1622499}
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