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Simplifying 0 = 4(x2) + -10x + -49 Reorder the terms: 0 = -49 + -10x + 4x2 Solving 0 = -49 + -10x + 4x2 Solving for variable 'x'. Combine like terms: 0 + 49 = 49 49 + 10x + -4x2 = -49 + -10x + 4x2 + 49 + 10x + -4x2 Reorder the terms: 49 + 10x + -4x2 = -49 + 49 + -10x + 10x + 4x2 + -4x2 Combine like terms: -49 + 49 = 0 49 + 10x + -4x2 = 0 + -10x + 10x + 4x2 + -4x2 49 + 10x + -4x2 = -10x + 10x + 4x2 + -4x2 Combine like terms: -10x + 10x = 0 49 + 10x + -4x2 = 0 + 4x2 + -4x2 49 + 10x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 49 + 10x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -12.25 + -2.5x + x2 = 0 Move the constant term to the right: Add '12.25' to each side of the equation. -12.25 + -2.5x + 12.25 + x2 = 0 + 12.25 Reorder the terms: -12.25 + 12.25 + -2.5x + x2 = 0 + 12.25 Combine like terms: -12.25 + 12.25 = 0.00 0.00 + -2.5x + x2 = 0 + 12.25 -2.5x + x2 = 0 + 12.25 Combine like terms: 0 + 12.25 = 12.25 -2.5x + x2 = 12.25 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 12.25 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 12.25 + 1.5625 Combine like terms: 12.25 + 1.5625 = 13.8125 1.5625 + -2.5x + x2 = 13.8125 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 13.8125 Calculate the square root of the right side: 3.716517187 Break this problem into two subproblems by setting (x + -1.25) equal to 3.716517187 and -3.716517187.Subproblem 1
x + -1.25 = 3.716517187 Simplifying x + -1.25 = 3.716517187 Reorder the terms: -1.25 + x = 3.716517187 Solving -1.25 + x = 3.716517187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 3.716517187 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 3.716517187 + 1.25 x = 3.716517187 + 1.25 Combine like terms: 3.716517187 + 1.25 = 4.966517187 x = 4.966517187 Simplifying x = 4.966517187Subproblem 2
x + -1.25 = -3.716517187 Simplifying x + -1.25 = -3.716517187 Reorder the terms: -1.25 + x = -3.716517187 Solving -1.25 + x = -3.716517187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -3.716517187 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -3.716517187 + 1.25 x = -3.716517187 + 1.25 Combine like terms: -3.716517187 + 1.25 = -2.466517187 x = -2.466517187 Simplifying x = -2.466517187Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.966517187, -2.466517187}
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