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Simplifying 16x2 + 6x + -4 = 21 Reorder the terms: -4 + 6x + 16x2 = 21 Solving -4 + 6x + 16x2 = 21 Solving for variable 'x'. Reorder the terms: -4 + -21 + 6x + 16x2 = 21 + -21 Combine like terms: -4 + -21 = -25 -25 + 6x + 16x2 = 21 + -21 Combine like terms: 21 + -21 = 0 -25 + 6x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -1.5625 + 0.375x + x2 = 0 Move the constant term to the right: Add '1.5625' to each side of the equation. -1.5625 + 0.375x + 1.5625 + x2 = 0 + 1.5625 Reorder the terms: -1.5625 + 1.5625 + 0.375x + x2 = 0 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + 0.375x + x2 = 0 + 1.5625 0.375x + x2 = 0 + 1.5625 Combine like terms: 0 + 1.5625 = 1.5625 0.375x + x2 = 1.5625 The x term is 0.375x. Take half its coefficient (0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. 0.375x + 0.03515625 + x2 = 1.5625 + 0.03515625 Reorder the terms: 0.03515625 + 0.375x + x2 = 1.5625 + 0.03515625 Combine like terms: 1.5625 + 0.03515625 = 1.59765625 0.03515625 + 0.375x + x2 = 1.59765625 Factor a perfect square on the left side: (x + 0.1875)(x + 0.1875) = 1.59765625 Calculate the square root of the right side: 1.263984276 Break this problem into two subproblems by setting (x + 0.1875) equal to 1.263984276 and -1.263984276.Subproblem 1
x + 0.1875 = 1.263984276 Simplifying x + 0.1875 = 1.263984276 Reorder the terms: 0.1875 + x = 1.263984276 Solving 0.1875 + x = 1.263984276 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = 1.263984276 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = 1.263984276 + -0.1875 x = 1.263984276 + -0.1875 Combine like terms: 1.263984276 + -0.1875 = 1.076484276 x = 1.076484276 Simplifying x = 1.076484276Subproblem 2
x + 0.1875 = -1.263984276 Simplifying x + 0.1875 = -1.263984276 Reorder the terms: 0.1875 + x = -1.263984276 Solving 0.1875 + x = -1.263984276 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = -1.263984276 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = -1.263984276 + -0.1875 x = -1.263984276 + -0.1875 Combine like terms: -1.263984276 + -0.1875 = -1.451484276 x = -1.451484276 Simplifying x = -1.451484276Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.076484276, -1.451484276}
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