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Simplifying 5.4x(x + -45) = 3x + 45 Reorder the terms: 5.4x(-45 + x) = 3x + 45 (-45 * 5.4x + x * 5.4x) = 3x + 45 (-243x + 5.4x2) = 3x + 45 Reorder the terms: -243x + 5.4x2 = 45 + 3x Solving -243x + 5.4x2 = 45 + 3x Solving for variable 'x'. Reorder the terms: -45 + -243x + -3x + 5.4x2 = 45 + 3x + -45 + -3x Combine like terms: -243x + -3x = -246x -45 + -246x + 5.4x2 = 45 + 3x + -45 + -3x Reorder the terms: -45 + -246x + 5.4x2 = 45 + -45 + 3x + -3x Combine like terms: 45 + -45 = 0 -45 + -246x + 5.4x2 = 0 + 3x + -3x -45 + -246x + 5.4x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -45 + -246x + 5.4x2 = 0 Begin completing the square. Divide all terms by 5.4 the coefficient of the squared term: Divide each side by '5.4'. -8.333333333 + -45.55555556x + x2 = 0 Move the constant term to the right: Add '8.333333333' to each side of the equation. -8.333333333 + -45.55555556x + 8.333333333 + x2 = 0 + 8.333333333 Reorder the terms: -8.333333333 + 8.333333333 + -45.55555556x + x2 = 0 + 8.333333333 Combine like terms: -8.333333333 + 8.333333333 = 0.000000000 0.000000000 + -45.55555556x + x2 = 0 + 8.333333333 -45.55555556x + x2 = 0 + 8.333333333 Combine like terms: 0 + 8.333333333 = 8.333333333 -45.55555556x + x2 = 8.333333333 The x term is -45.55555556x. Take half its coefficient (-22.77777778). Square it (518.8271606) and add it to both sides. Add '518.8271606' to each side of the equation. -45.55555556x + 518.8271606 + x2 = 8.333333333 + 518.8271606 Reorder the terms: 518.8271606 + -45.55555556x + x2 = 8.333333333 + 518.8271606 Combine like terms: 8.333333333 + 518.8271606 = 527.160493933 518.8271606 + -45.55555556x + x2 = 527.160493933 Factor a perfect square on the left side: (x + -22.77777778)(x + -22.77777778) = 527.160493933 Calculate the square root of the right side: 22.959975913 Break this problem into two subproblems by setting (x + -22.77777778) equal to 22.959975913 and -22.959975913.Subproblem 1
x + -22.77777778 = 22.959975913 Simplifying x + -22.77777778 = 22.959975913 Reorder the terms: -22.77777778 + x = 22.959975913 Solving -22.77777778 + x = 22.959975913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.77777778' to each side of the equation. -22.77777778 + 22.77777778 + x = 22.959975913 + 22.77777778 Combine like terms: -22.77777778 + 22.77777778 = 0.00000000 0.00000000 + x = 22.959975913 + 22.77777778 x = 22.959975913 + 22.77777778 Combine like terms: 22.959975913 + 22.77777778 = 45.737753693 x = 45.737753693 Simplifying x = 45.737753693Subproblem 2
x + -22.77777778 = -22.959975913 Simplifying x + -22.77777778 = -22.959975913 Reorder the terms: -22.77777778 + x = -22.959975913 Solving -22.77777778 + x = -22.959975913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.77777778' to each side of the equation. -22.77777778 + 22.77777778 + x = -22.959975913 + 22.77777778 Combine like terms: -22.77777778 + 22.77777778 = 0.00000000 0.00000000 + x = -22.959975913 + 22.77777778 x = -22.959975913 + 22.77777778 Combine like terms: -22.959975913 + 22.77777778 = -0.182198133 x = -0.182198133 Simplifying x = -0.182198133Solution
The solution to the problem is based on the solutions from the subproblems. x = {45.737753693, -0.182198133}
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