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Simplifying 4x2 + -4x + -47 = 0 Reorder the terms: -47 + -4x + 4x2 = 0 Solving -47 + -4x + 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'. -11.75 + -1x + x2 = 0 Move the constant term to the right: Add '11.75' to each side of the equation. -11.75 + -1x + 11.75 + x2 = 0 + 11.75 Reorder the terms: -11.75 + 11.75 + -1x + x2 = 0 + 11.75 Combine like terms: -11.75 + 11.75 = 0.00 0.00 + -1x + x2 = 0 + 11.75 -1x + x2 = 0 + 11.75 Combine like terms: 0 + 11.75 = 11.75 -1x + x2 = 11.75 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 11.75 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 11.75 + 0.25 Combine like terms: 11.75 + 0.25 = 12 0.25 + -1x + x2 = 12 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + -0.5) equal to 3.464101615 and -3.464101615.Subproblem 1
x + -0.5 = 3.464101615 Simplifying x + -0.5 = 3.464101615 Reorder the terms: -0.5 + x = 3.464101615 Solving -0.5 + x = 3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 3.464101615 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 3.464101615 + 0.5 x = 3.464101615 + 0.5 Combine like terms: 3.464101615 + 0.5 = 3.964101615 x = 3.964101615 Simplifying x = 3.964101615Subproblem 2
x + -0.5 = -3.464101615 Simplifying x + -0.5 = -3.464101615 Reorder the terms: -0.5 + x = -3.464101615 Solving -0.5 + x = -3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -3.464101615 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -3.464101615 + 0.5 x = -3.464101615 + 0.5 Combine like terms: -3.464101615 + 0.5 = -2.964101615 x = -2.964101615 Simplifying x = -2.964101615Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.964101615, -2.964101615}
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