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Simplifying 7x2 + 12x + -16 = 0 Reorder the terms: -16 + 12x + 7x2 = 0 Solving -16 + 12x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.285714286 + 1.714285714x + x2 = 0 Move the constant term to the right: Add '2.285714286' to each side of the equation. -2.285714286 + 1.714285714x + 2.285714286 + x2 = 0 + 2.285714286 Reorder the terms: -2.285714286 + 2.285714286 + 1.714285714x + x2 = 0 + 2.285714286 Combine like terms: -2.285714286 + 2.285714286 = 0.000000000 0.000000000 + 1.714285714x + x2 = 0 + 2.285714286 1.714285714x + x2 = 0 + 2.285714286 Combine like terms: 0 + 2.285714286 = 2.285714286 1.714285714x + x2 = 2.285714286 The x term is 1.714285714x. Take half its coefficient (0.857142857). Square it (0.7346938773) and add it to both sides. Add '0.7346938773' to each side of the equation. 1.714285714x + 0.7346938773 + x2 = 2.285714286 + 0.7346938773 Reorder the terms: 0.7346938773 + 1.714285714x + x2 = 2.285714286 + 0.7346938773 Combine like terms: 2.285714286 + 0.7346938773 = 3.0204081633 0.7346938773 + 1.714285714x + x2 = 3.0204081633 Factor a perfect square on the left side: (x + 0.857142857)(x + 0.857142857) = 3.0204081633 Calculate the square root of the right side: 1.737932152 Break this problem into two subproblems by setting (x + 0.857142857) equal to 1.737932152 and -1.737932152.Subproblem 1
x + 0.857142857 = 1.737932152 Simplifying x + 0.857142857 = 1.737932152 Reorder the terms: 0.857142857 + x = 1.737932152 Solving 0.857142857 + x = 1.737932152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.857142857' to each side of the equation. 0.857142857 + -0.857142857 + x = 1.737932152 + -0.857142857 Combine like terms: 0.857142857 + -0.857142857 = 0.000000000 0.000000000 + x = 1.737932152 + -0.857142857 x = 1.737932152 + -0.857142857 Combine like terms: 1.737932152 + -0.857142857 = 0.880789295 x = 0.880789295 Simplifying x = 0.880789295Subproblem 2
x + 0.857142857 = -1.737932152 Simplifying x + 0.857142857 = -1.737932152 Reorder the terms: 0.857142857 + x = -1.737932152 Solving 0.857142857 + x = -1.737932152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.857142857' to each side of the equation. 0.857142857 + -0.857142857 + x = -1.737932152 + -0.857142857 Combine like terms: 0.857142857 + -0.857142857 = 0.000000000 0.000000000 + x = -1.737932152 + -0.857142857 x = -1.737932152 + -0.857142857 Combine like terms: -1.737932152 + -0.857142857 = -2.595075009 x = -2.595075009 Simplifying x = -2.595075009Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.880789295, -2.595075009}
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