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Simplifying -4x2 + 12x + -7 = 0 Reorder the terms: -7 + 12x + -4x2 = 0 Solving -7 + 12x + -4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 1.75 + -3x + x2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + -3x + -1.75 + x2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + -3x + x2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + -3x + x2 = 0 + -1.75 -3x + x2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 -3x + x2 = -1.75 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 = -1.75 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -1.75 + 2.25 Combine like terms: -1.75 + 2.25 = 0.5 2.25 + -3x + x2 = 0.5 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 0.5 Calculate the square root of the right side: 0.707106781 Break this problem into two subproblems by setting (x + -1.5) equal to 0.707106781 and -0.707106781.Subproblem 1
x + -1.5 = 0.707106781 Simplifying x + -1.5 = 0.707106781 Reorder the terms: -1.5 + x = 0.707106781 Solving -1.5 + x = 0.707106781 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 = 0.707106781 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 0.707106781 + 1.5 x = 0.707106781 + 1.5 Combine like terms: 0.707106781 + 1.5 = 2.207106781 x = 2.207106781 Simplifying x = 2.207106781Subproblem 2
x + -1.5 = -0.707106781 Simplifying x + -1.5 = -0.707106781 Reorder the terms: -1.5 + x = -0.707106781 Solving -1.5 + x = -0.707106781 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 = -0.707106781 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -0.707106781 + 1.5 x = -0.707106781 + 1.5 Combine like terms: -0.707106781 + 1.5 = 0.792893219 x = 0.792893219 Simplifying x = 0.792893219Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.207106781, 0.792893219}
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