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Simplifying 16x + -64 + 6x2 = 7x Reorder the terms: -64 + 16x + 6x2 = 7x Solving -64 + 16x + 6x2 = 7x Solving for variable 'x'. Reorder the terms: -64 + 16x + -7x + 6x2 = 7x + -7x Combine like terms: 16x + -7x = 9x -64 + 9x + 6x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -64 + 9x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -10.66666667 + 1.5x + x2 = 0 Move the constant term to the right: Add '10.66666667' to each side of the equation. -10.66666667 + 1.5x + 10.66666667 + x2 = 0 + 10.66666667 Reorder the terms: -10.66666667 + 10.66666667 + 1.5x + x2 = 0 + 10.66666667 Combine like terms: -10.66666667 + 10.66666667 = 0.00000000 0.00000000 + 1.5x + x2 = 0 + 10.66666667 1.5x + x2 = 0 + 10.66666667 Combine like terms: 0 + 10.66666667 = 10.66666667 1.5x + x2 = 10.66666667 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 10.66666667 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 10.66666667 + 0.5625 Combine like terms: 10.66666667 + 0.5625 = 11.22916667 0.5625 + 1.5x + x2 = 11.22916667 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 11.22916667 Calculate the square root of the right side: 3.350994878 Break this problem into two subproblems by setting (x + 0.75) equal to 3.350994878 and -3.350994878.Subproblem 1
x + 0.75 = 3.350994878 Simplifying x + 0.75 = 3.350994878 Reorder the terms: 0.75 + x = 3.350994878 Solving 0.75 + x = 3.350994878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 3.350994878 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 3.350994878 + -0.75 x = 3.350994878 + -0.75 Combine like terms: 3.350994878 + -0.75 = 2.600994878 x = 2.600994878 Simplifying x = 2.600994878Subproblem 2
x + 0.75 = -3.350994878 Simplifying x + 0.75 = -3.350994878 Reorder the terms: 0.75 + x = -3.350994878 Solving 0.75 + x = -3.350994878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -3.350994878 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -3.350994878 + -0.75 x = -3.350994878 + -0.75 Combine like terms: -3.350994878 + -0.75 = -4.100994878 x = -4.100994878 Simplifying x = -4.100994878Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.600994878, -4.100994878}
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