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Simplifying -7x + 8x(36x) + 19 = 99 Remove parenthesis around (36x) -7x + 8x * 36x + 19 = 99 Reorder the terms for easier multiplication: -7x + 8 * 36x * x + 19 = 99 Multiply 8 * 36 -7x + 288x * x + 19 = 99 Multiply x * x -7x + 288x2 + 19 = 99 Reorder the terms: 19 + -7x + 288x2 = 99 Solving 19 + -7x + 288x2 = 99 Solving for variable 'x'. Reorder the terms: 19 + -99 + -7x + 288x2 = 99 + -99 Combine like terms: 19 + -99 = -80 -80 + -7x + 288x2 = 99 + -99 Combine like terms: 99 + -99 = 0 -80 + -7x + 288x2 = 0 Begin completing the square. Divide all terms by 288 the coefficient of the squared term: Divide each side by '288'. -0.2777777778 + -0.02430555556x + x2 = 0 Move the constant term to the right: Add '0.2777777778' to each side of the equation. -0.2777777778 + -0.02430555556x + 0.2777777778 + x2 = 0 + 0.2777777778 Reorder the terms: -0.2777777778 + 0.2777777778 + -0.02430555556x + x2 = 0 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + -0.02430555556x + x2 = 0 + 0.2777777778 -0.02430555556x + x2 = 0 + 0.2777777778 Combine like terms: 0 + 0.2777777778 = 0.2777777778 -0.02430555556x + x2 = 0.2777777778 The x term is -0.02430555556x. Take half its coefficient (-0.01215277778). Square it (0.0001476900078) and add it to both sides. Add '0.0001476900078' to each side of the equation. -0.02430555556x + 0.0001476900078 + x2 = 0.2777777778 + 0.0001476900078 Reorder the terms: 0.0001476900078 + -0.02430555556x + x2 = 0.2777777778 + 0.0001476900078 Combine like terms: 0.2777777778 + 0.0001476900078 = 0.2779254678078 0.0001476900078 + -0.02430555556x + x2 = 0.2779254678078 Factor a perfect square on the left side: (x + -0.01215277778)(x + -0.01215277778) = 0.2779254678078 Calculate the square root of the right side: 0.527186369 Break this problem into two subproblems by setting (x + -0.01215277778) equal to 0.527186369 and -0.527186369.Subproblem 1
x + -0.01215277778 = 0.527186369 Simplifying x + -0.01215277778 = 0.527186369 Reorder the terms: -0.01215277778 + x = 0.527186369 Solving -0.01215277778 + x = 0.527186369 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01215277778' to each side of the equation. -0.01215277778 + 0.01215277778 + x = 0.527186369 + 0.01215277778 Combine like terms: -0.01215277778 + 0.01215277778 = 0.00000000000 0.00000000000 + x = 0.527186369 + 0.01215277778 x = 0.527186369 + 0.01215277778 Combine like terms: 0.527186369 + 0.01215277778 = 0.53933914678 x = 0.53933914678 Simplifying x = 0.53933914678Subproblem 2
x + -0.01215277778 = -0.527186369 Simplifying x + -0.01215277778 = -0.527186369 Reorder the terms: -0.01215277778 + x = -0.527186369 Solving -0.01215277778 + x = -0.527186369 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01215277778' to each side of the equation. -0.01215277778 + 0.01215277778 + x = -0.527186369 + 0.01215277778 Combine like terms: -0.01215277778 + 0.01215277778 = 0.00000000000 0.00000000000 + x = -0.527186369 + 0.01215277778 x = -0.527186369 + 0.01215277778 Combine like terms: -0.527186369 + 0.01215277778 = -0.51503359122 x = -0.51503359122 Simplifying x = -0.51503359122Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.53933914678, -0.51503359122}
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