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Simplifying x2 + 4x2 + 24x + -36 = 9 Reorder the terms: -36 + 24x + x2 + 4x2 = 9 Combine like terms: x2 + 4x2 = 5x2 -36 + 24x + 5x2 = 9 Solving -36 + 24x + 5x2 = 9 Solving for variable 'x'. Reorder the terms: -36 + -9 + 24x + 5x2 = 9 + -9 Combine like terms: -36 + -9 = -45 -45 + 24x + 5x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -45 + 24x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -9 + 4.8x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 4.8x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 4.8x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 4.8x + x2 = 0 + 9 4.8x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 4.8x + x2 = 9 The x term is 4.8x. Take half its coefficient (2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. 4.8x + 5.76 + x2 = 9 + 5.76 Reorder the terms: 5.76 + 4.8x + x2 = 9 + 5.76 Combine like terms: 9 + 5.76 = 14.76 5.76 + 4.8x + x2 = 14.76 Factor a perfect square on the left side: (x + 2.4)(x + 2.4) = 14.76 Calculate the square root of the right side: 3.841874542 Break this problem into two subproblems by setting (x + 2.4) equal to 3.841874542 and -3.841874542.Subproblem 1
x + 2.4 = 3.841874542 Simplifying x + 2.4 = 3.841874542 Reorder the terms: 2.4 + x = 3.841874542 Solving 2.4 + x = 3.841874542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + x = 3.841874542 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + x = 3.841874542 + -2.4 x = 3.841874542 + -2.4 Combine like terms: 3.841874542 + -2.4 = 1.441874542 x = 1.441874542 Simplifying x = 1.441874542Subproblem 2
x + 2.4 = -3.841874542 Simplifying x + 2.4 = -3.841874542 Reorder the terms: 2.4 + x = -3.841874542 Solving 2.4 + x = -3.841874542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + x = -3.841874542 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + x = -3.841874542 + -2.4 x = -3.841874542 + -2.4 Combine like terms: -3.841874542 + -2.4 = -6.241874542 x = -6.241874542 Simplifying x = -6.241874542Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.441874542, -6.241874542}
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