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Simplifying -16x2 + 5216x + 119471 = 0 Reorder the terms: 119471 + 5216x + -16x2 = 0 Solving 119471 + 5216x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -7466.9375 + -326x + x2 = 0 Move the constant term to the right: Add '7466.9375' to each side of the equation. -7466.9375 + -326x + 7466.9375 + x2 = 0 + 7466.9375 Reorder the terms: -7466.9375 + 7466.9375 + -326x + x2 = 0 + 7466.9375 Combine like terms: -7466.9375 + 7466.9375 = 0.0000 0.0000 + -326x + x2 = 0 + 7466.9375 -326x + x2 = 0 + 7466.9375 Combine like terms: 0 + 7466.9375 = 7466.9375 -326x + x2 = 7466.9375 The x term is -326x. Take half its coefficient (-163). Square it (26569) and add it to both sides. Add '26569' to each side of the equation. -326x + 26569 + x2 = 7466.9375 + 26569 Reorder the terms: 26569 + -326x + x2 = 7466.9375 + 26569 Combine like terms: 7466.9375 + 26569 = 34035.9375 26569 + -326x + x2 = 34035.9375 Factor a perfect square on the left side: (x + -163)(x + -163) = 34035.9375 Calculate the square root of the right side: 184.488312638 Break this problem into two subproblems by setting (x + -163) equal to 184.488312638 and -184.488312638.Subproblem 1
x + -163 = 184.488312638 Simplifying x + -163 = 184.488312638 Reorder the terms: -163 + x = 184.488312638 Solving -163 + x = 184.488312638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '163' to each side of the equation. -163 + 163 + x = 184.488312638 + 163 Combine like terms: -163 + 163 = 0 0 + x = 184.488312638 + 163 x = 184.488312638 + 163 Combine like terms: 184.488312638 + 163 = 347.488312638 x = 347.488312638 Simplifying x = 347.488312638Subproblem 2
x + -163 = -184.488312638 Simplifying x + -163 = -184.488312638 Reorder the terms: -163 + x = -184.488312638 Solving -163 + x = -184.488312638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '163' to each side of the equation. -163 + 163 + x = -184.488312638 + 163 Combine like terms: -163 + 163 = 0 0 + x = -184.488312638 + 163 x = -184.488312638 + 163 Combine like terms: -184.488312638 + 163 = -21.488312638 x = -21.488312638 Simplifying x = -21.488312638Solution
The solution to the problem is based on the solutions from the subproblems. x = {347.488312638, -21.488312638}
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