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Simplifying -4.9x2 + 19.6x + 58.8 = 70 Reorder the terms: 58.8 + 19.6x + -4.9x2 = 70 Solving 58.8 + 19.6x + -4.9x2 = 70 Solving for variable 'x'. Reorder the terms: 58.8 + -70 + 19.6x + -4.9x2 = 70 + -70 Combine like terms: 58.8 + -70 = -11.2 -11.2 + 19.6x + -4.9x2 = 70 + -70 Combine like terms: 70 + -70 = 0 -11.2 + 19.6x + -4.9x2 = 0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. 2.285714286 + -4x + x2 = 0 Move the constant term to the right: Add '-2.285714286' to each side of the equation. 2.285714286 + -4x + -2.285714286 + x2 = 0 + -2.285714286 Reorder the terms: 2.285714286 + -2.285714286 + -4x + x2 = 0 + -2.285714286 Combine like terms: 2.285714286 + -2.285714286 = 0.000000000 0.000000000 + -4x + x2 = 0 + -2.285714286 -4x + x2 = 0 + -2.285714286 Combine like terms: 0 + -2.285714286 = -2.285714286 -4x + x2 = -2.285714286 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -2.285714286 + 4 Reorder the terms: 4 + -4x + x2 = -2.285714286 + 4 Combine like terms: -2.285714286 + 4 = 1.714285714 4 + -4x + x2 = 1.714285714 Factor a perfect square on the left side: (x + -2)(x + -2) = 1.714285714 Calculate the square root of the right side: 1.309307341 Break this problem into two subproblems by setting (x + -2) equal to 1.309307341 and -1.309307341.Subproblem 1
x + -2 = 1.309307341 Simplifying x + -2 = 1.309307341 Reorder the terms: -2 + x = 1.309307341 Solving -2 + x = 1.309307341 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.309307341 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.309307341 + 2 x = 1.309307341 + 2 Combine like terms: 1.309307341 + 2 = 3.309307341 x = 3.309307341 Simplifying x = 3.309307341Subproblem 2
x + -2 = -1.309307341 Simplifying x + -2 = -1.309307341 Reorder the terms: -2 + x = -1.309307341 Solving -2 + x = -1.309307341 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.309307341 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.309307341 + 2 x = -1.309307341 + 2 Combine like terms: -1.309307341 + 2 = 0.690692659 x = 0.690692659 Simplifying x = 0.690692659Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.309307341, 0.690692659}
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