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Simplifying 40x = 7x2 + -29x + -30 Reorder the terms: 40x = -30 + -29x + 7x2 Solving 40x = -30 + -29x + 7x2 Solving for variable 'x'. Reorder the terms: 30 + 40x + 29x + -7x2 = -30 + -29x + 7x2 + 30 + 29x + -7x2 Combine like terms: 40x + 29x = 69x 30 + 69x + -7x2 = -30 + -29x + 7x2 + 30 + 29x + -7x2 Reorder the terms: 30 + 69x + -7x2 = -30 + 30 + -29x + 29x + 7x2 + -7x2 Combine like terms: -30 + 30 = 0 30 + 69x + -7x2 = 0 + -29x + 29x + 7x2 + -7x2 30 + 69x + -7x2 = -29x + 29x + 7x2 + -7x2 Combine like terms: -29x + 29x = 0 30 + 69x + -7x2 = 0 + 7x2 + -7x2 30 + 69x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 30 + 69x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -4.285714286 + -9.857142857x + x2 = 0 Move the constant term to the right: Add '4.285714286' to each side of the equation. -4.285714286 + -9.857142857x + 4.285714286 + x2 = 0 + 4.285714286 Reorder the terms: -4.285714286 + 4.285714286 + -9.857142857x + x2 = 0 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + -9.857142857x + x2 = 0 + 4.285714286 -9.857142857x + x2 = 0 + 4.285714286 Combine like terms: 0 + 4.285714286 = 4.285714286 -9.857142857x + x2 = 4.285714286 The x term is -9.857142857x. Take half its coefficient (-4.928571429). Square it (24.29081633) and add it to both sides. Add '24.29081633' to each side of the equation. -9.857142857x + 24.29081633 + x2 = 4.285714286 + 24.29081633 Reorder the terms: 24.29081633 + -9.857142857x + x2 = 4.285714286 + 24.29081633 Combine like terms: 4.285714286 + 24.29081633 = 28.576530616 24.29081633 + -9.857142857x + x2 = 28.576530616 Factor a perfect square on the left side: (x + -4.928571429)(x + -4.928571429) = 28.576530616 Calculate the square root of the right side: 5.34570207 Break this problem into two subproblems by setting (x + -4.928571429) equal to 5.34570207 and -5.34570207.Subproblem 1
x + -4.928571429 = 5.34570207 Simplifying x + -4.928571429 = 5.34570207 Reorder the terms: -4.928571429 + x = 5.34570207 Solving -4.928571429 + x = 5.34570207 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.928571429' to each side of the equation. -4.928571429 + 4.928571429 + x = 5.34570207 + 4.928571429 Combine like terms: -4.928571429 + 4.928571429 = 0.000000000 0.000000000 + x = 5.34570207 + 4.928571429 x = 5.34570207 + 4.928571429 Combine like terms: 5.34570207 + 4.928571429 = 10.274273499 x = 10.274273499 Simplifying x = 10.274273499Subproblem 2
x + -4.928571429 = -5.34570207 Simplifying x + -4.928571429 = -5.34570207 Reorder the terms: -4.928571429 + x = -5.34570207 Solving -4.928571429 + x = -5.34570207 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.928571429' to each side of the equation. -4.928571429 + 4.928571429 + x = -5.34570207 + 4.928571429 Combine like terms: -4.928571429 + 4.928571429 = 0.000000000 0.000000000 + x = -5.34570207 + 4.928571429 x = -5.34570207 + 4.928571429 Combine like terms: -5.34570207 + 4.928571429 = -0.417130641 x = -0.417130641 Simplifying x = -0.417130641Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.274273499, -0.417130641}
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