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Simplifying 4x2 + -12x = 15 Reorder the terms: -12x + 4x2 = 15 Solving -12x + 4x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + -12x + 4x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + -12x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + -3x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -3x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -3x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -3x + x2 = 0 + 3.75 -3x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -3x + x2 = 3.75 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 3.75 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 3.75 + 2.25 Combine like terms: 3.75 + 2.25 = 6 2.25 + -3x + x2 = 6 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + -1.5) equal to 2.449489743 and -2.449489743.Subproblem 1
x + -1.5 = 2.449489743 Simplifying x + -1.5 = 2.449489743 Reorder the terms: -1.5 + x = 2.449489743 Solving -1.5 + x = 2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 2.449489743 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.449489743 + 1.5 x = 2.449489743 + 1.5 Combine like terms: 2.449489743 + 1.5 = 3.949489743 x = 3.949489743 Simplifying x = 3.949489743Subproblem 2
x + -1.5 = -2.449489743 Simplifying x + -1.5 = -2.449489743 Reorder the terms: -1.5 + x = -2.449489743 Solving -1.5 + x = -2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -2.449489743 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.449489743 + 1.5 x = -2.449489743 + 1.5 Combine like terms: -2.449489743 + 1.5 = -0.949489743 x = -0.949489743 Simplifying x = -0.949489743Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.949489743, -0.949489743}
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