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Simplifying -25x2 + -2x + 9 = 0 Reorder the terms: 9 + -2x + -25x2 = 0 Solving 9 + -2x + -25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -25 the coefficient of the squared term: Divide each side by '-25'. -0.36 + 0.08x + x2 = 0 Move the constant term to the right: Add '0.36' to each side of the equation. -0.36 + 0.08x + 0.36 + x2 = 0 + 0.36 Reorder the terms: -0.36 + 0.36 + 0.08x + x2 = 0 + 0.36 Combine like terms: -0.36 + 0.36 = 0.00 0.00 + 0.08x + x2 = 0 + 0.36 0.08x + x2 = 0 + 0.36 Combine like terms: 0 + 0.36 = 0.36 0.08x + x2 = 0.36 The x term is 0.08x. Take half its coefficient (0.04). Square it (0.0016) and add it to both sides. Add '0.0016' to each side of the equation. 0.08x + 0.0016 + x2 = 0.36 + 0.0016 Reorder the terms: 0.0016 + 0.08x + x2 = 0.36 + 0.0016 Combine like terms: 0.36 + 0.0016 = 0.3616 0.0016 + 0.08x + x2 = 0.3616 Factor a perfect square on the left side: (x + 0.04)(x + 0.04) = 0.3616 Calculate the square root of the right side: 0.601331855 Break this problem into two subproblems by setting (x + 0.04) equal to 0.601331855 and -0.601331855.Subproblem 1
x + 0.04 = 0.601331855 Simplifying x + 0.04 = 0.601331855 Reorder the terms: 0.04 + x = 0.601331855 Solving 0.04 + x = 0.601331855 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04' to each side of the equation. 0.04 + -0.04 + x = 0.601331855 + -0.04 Combine like terms: 0.04 + -0.04 = 0.00 0.00 + x = 0.601331855 + -0.04 x = 0.601331855 + -0.04 Combine like terms: 0.601331855 + -0.04 = 0.561331855 x = 0.561331855 Simplifying x = 0.561331855Subproblem 2
x + 0.04 = -0.601331855 Simplifying x + 0.04 = -0.601331855 Reorder the terms: 0.04 + x = -0.601331855 Solving 0.04 + x = -0.601331855 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04' to each side of the equation. 0.04 + -0.04 + x = -0.601331855 + -0.04 Combine like terms: 0.04 + -0.04 = 0.00 0.00 + x = -0.601331855 + -0.04 x = -0.601331855 + -0.04 Combine like terms: -0.601331855 + -0.04 = -0.641331855 x = -0.641331855 Simplifying x = -0.641331855Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.561331855, -0.641331855}
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