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Simplifying 2x2 + -16x + 21 = 0 Reorder the terms: 21 + -16x + 2x2 = 0 Solving 21 + -16x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 10.5 + -8x + x2 = 0 Move the constant term to the right: Add '-10.5' to each side of the equation. 10.5 + -8x + -10.5 + x2 = 0 + -10.5 Reorder the terms: 10.5 + -10.5 + -8x + x2 = 0 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + -8x + x2 = 0 + -10.5 -8x + x2 = 0 + -10.5 Combine like terms: 0 + -10.5 = -10.5 -8x + x2 = -10.5 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -10.5 + 16 Reorder the terms: 16 + -8x + x2 = -10.5 + 16 Combine like terms: -10.5 + 16 = 5.5 16 + -8x + x2 = 5.5 Factor a perfect square on the left side: (x + -4)(x + -4) = 5.5 Calculate the square root of the right side: 2.34520788 Break this problem into two subproblems by setting (x + -4) equal to 2.34520788 and -2.34520788.Subproblem 1
x + -4 = 2.34520788 Simplifying x + -4 = 2.34520788 Reorder the terms: -4 + x = 2.34520788 Solving -4 + x = 2.34520788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 2.34520788 + 4 Combine like terms: -4 + 4 = 0 0 + x = 2.34520788 + 4 x = 2.34520788 + 4 Combine like terms: 2.34520788 + 4 = 6.34520788 x = 6.34520788 Simplifying x = 6.34520788Subproblem 2
x + -4 = -2.34520788 Simplifying x + -4 = -2.34520788 Reorder the terms: -4 + x = -2.34520788 Solving -4 + x = -2.34520788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -2.34520788 + 4 Combine like terms: -4 + 4 = 0 0 + x = -2.34520788 + 4 x = -2.34520788 + 4 Combine like terms: -2.34520788 + 4 = 1.65479212 x = 1.65479212 Simplifying x = 1.65479212Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.34520788, 1.65479212}
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