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Simplifying (-62 + 6x)(64 + 6x) = 28 * 140 Multiply (-62 + 6x) * (64 + 6x) (-62(64 + 6x) + 6x * (64 + 6x)) = 28 * 140 ((64 * -62 + 6x * -62) + 6x * (64 + 6x)) = 28 * 140 ((-3968 + -372x) + 6x * (64 + 6x)) = 28 * 140 (-3968 + -372x + (64 * 6x + 6x * 6x)) = 28 * 140 (-3968 + -372x + (384x + 36x2)) = 28 * 140 Combine like terms: -372x + 384x = 12x (-3968 + 12x + 36x2) = 28 * 140 Multiply 28 * 140 -3968 + 12x + 36x2 = 3920 Solving -3968 + 12x + 36x2 = 3920 Solving for variable 'x'. Reorder the terms: -3968 + -3920 + 12x + 36x2 = 3920 + -3920 Combine like terms: -3968 + -3920 = -7888 -7888 + 12x + 36x2 = 3920 + -3920 Combine like terms: 3920 + -3920 = 0 -7888 + 12x + 36x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-1972 + 3x + 9x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1972 + 3x + 9x2)' equal to zero and attempt to solve: Simplifying -1972 + 3x + 9x2 = 0 Solving -1972 + 3x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -219.1111111 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '219.1111111' to each side of the equation. -219.1111111 + 0.3333333333x + 219.1111111 + x2 = 0 + 219.1111111 Reorder the terms: -219.1111111 + 219.1111111 + 0.3333333333x + x2 = 0 + 219.1111111 Combine like terms: -219.1111111 + 219.1111111 = 0.0000000 0.0000000 + 0.3333333333x + x2 = 0 + 219.1111111 0.3333333333x + x2 = 0 + 219.1111111 Combine like terms: 0 + 219.1111111 = 219.1111111 0.3333333333x + x2 = 219.1111111 The x term is 0.3333333333x. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333x + 0.02777777779 + x2 = 219.1111111 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = 219.1111111 + 0.02777777779 Combine like terms: 219.1111111 + 0.02777777779 = 219.13888887779 0.02777777779 + 0.3333333333x + x2 = 219.13888887779 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 219.13888887779 Calculate the square root of the right side: 14.803340463 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 14.803340463 and -14.803340463.Subproblem 1
x + 0.1666666667 = 14.803340463 Simplifying x + 0.1666666667 = 14.803340463 Reorder the terms: 0.1666666667 + x = 14.803340463 Solving 0.1666666667 + x = 14.803340463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = 14.803340463 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 14.803340463 + -0.1666666667 x = 14.803340463 + -0.1666666667 Combine like terms: 14.803340463 + -0.1666666667 = 14.6366737963 x = 14.6366737963 Simplifying x = 14.6366737963Subproblem 2
x + 0.1666666667 = -14.803340463 Simplifying x + 0.1666666667 = -14.803340463 Reorder the terms: 0.1666666667 + x = -14.803340463 Solving 0.1666666667 + x = -14.803340463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = -14.803340463 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -14.803340463 + -0.1666666667 x = -14.803340463 + -0.1666666667 Combine like terms: -14.803340463 + -0.1666666667 = -14.9700071297 x = -14.9700071297 Simplifying x = -14.9700071297Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.6366737963, -14.9700071297}Solution
x = {14.6366737963, -14.9700071297}
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