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Simplifying 5x2 + -16x + -52 = 9 Reorder the terms: -52 + -16x + 5x2 = 9 Solving -52 + -16x + 5x2 = 9 Solving for variable 'x'. Reorder the terms: -52 + -9 + -16x + 5x2 = 9 + -9 Combine like terms: -52 + -9 = -61 -61 + -16x + 5x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -61 + -16x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -12.2 + -3.2x + x2 = 0 Move the constant term to the right: Add '12.2' to each side of the equation. -12.2 + -3.2x + 12.2 + x2 = 0 + 12.2 Reorder the terms: -12.2 + 12.2 + -3.2x + x2 = 0 + 12.2 Combine like terms: -12.2 + 12.2 = 0.0 0.0 + -3.2x + x2 = 0 + 12.2 -3.2x + x2 = 0 + 12.2 Combine like terms: 0 + 12.2 = 12.2 -3.2x + x2 = 12.2 The x term is -3.2x. Take half its coefficient (-1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. -3.2x + 2.56 + x2 = 12.2 + 2.56 Reorder the terms: 2.56 + -3.2x + x2 = 12.2 + 2.56 Combine like terms: 12.2 + 2.56 = 14.76 2.56 + -3.2x + x2 = 14.76 Factor a perfect square on the left side: (x + -1.6)(x + -1.6) = 14.76 Calculate the square root of the right side: 3.841874542 Break this problem into two subproblems by setting (x + -1.6) equal to 3.841874542 and -3.841874542.Subproblem 1
x + -1.6 = 3.841874542 Simplifying x + -1.6 = 3.841874542 Reorder the terms: -1.6 + x = 3.841874542 Solving -1.6 + x = 3.841874542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = 3.841874542 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = 3.841874542 + 1.6 x = 3.841874542 + 1.6 Combine like terms: 3.841874542 + 1.6 = 5.441874542 x = 5.441874542 Simplifying x = 5.441874542Subproblem 2
x + -1.6 = -3.841874542 Simplifying x + -1.6 = -3.841874542 Reorder the terms: -1.6 + x = -3.841874542 Solving -1.6 + x = -3.841874542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = -3.841874542 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = -3.841874542 + 1.6 x = -3.841874542 + 1.6 Combine like terms: -3.841874542 + 1.6 = -2.241874542 x = -2.241874542 Simplifying x = -2.241874542Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.441874542, -2.241874542}
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