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Simplifying 4x2 + -12x + 8 = 7 Reorder the terms: 8 + -12x + 4x2 = 7 Solving 8 + -12x + 4x2 = 7 Solving for variable 'x'. Reorder the terms: 8 + -7 + -12x + 4x2 = 7 + -7 Combine like terms: 8 + -7 = 1 1 + -12x + 4x2 = 7 + -7 Combine like terms: 7 + -7 = 0 1 + -12x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + -3x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -3x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -3x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -3x + x2 = 0 + -0.25 -3x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -3x + x2 = -0.25 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 = -0.25 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -0.25 + 2.25 Combine like terms: -0.25 + 2.25 = 2 2.25 + -3x + x2 = 2 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + -1.5) equal to 1.414213562 and -1.414213562.Subproblem 1
x + -1.5 = 1.414213562 Simplifying x + -1.5 = 1.414213562 Reorder the terms: -1.5 + x = 1.414213562 Solving -1.5 + x = 1.414213562 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 = 1.414213562 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.414213562 + 1.5 x = 1.414213562 + 1.5 Combine like terms: 1.414213562 + 1.5 = 2.914213562 x = 2.914213562 Simplifying x = 2.914213562Subproblem 2
x + -1.5 = -1.414213562 Simplifying x + -1.5 = -1.414213562 Reorder the terms: -1.5 + x = -1.414213562 Solving -1.5 + x = -1.414213562 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 = -1.414213562 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.414213562 + 1.5 x = -1.414213562 + 1.5 Combine like terms: -1.414213562 + 1.5 = 0.085786438 x = 0.085786438 Simplifying x = 0.085786438Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.914213562, 0.085786438}
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