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Simplifying -10x2 + -4x + 9 = 0 Reorder the terms: 9 + -4x + -10x2 = 0 Solving 9 + -4x + -10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -0.9 + 0.4x + x2 = 0 Move the constant term to the right: Add '0.9' to each side of the equation. -0.9 + 0.4x + 0.9 + x2 = 0 + 0.9 Reorder the terms: -0.9 + 0.9 + 0.4x + x2 = 0 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + 0.4x + x2 = 0 + 0.9 0.4x + x2 = 0 + 0.9 Combine like terms: 0 + 0.9 = 0.9 0.4x + x2 = 0.9 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 0.9 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 0.9 + 0.04 Combine like terms: 0.9 + 0.04 = 0.94 0.04 + 0.4x + x2 = 0.94 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 0.94 Calculate the square root of the right side: 0.969535971 Break this problem into two subproblems by setting (x + 0.2) equal to 0.969535971 and -0.969535971.Subproblem 1
x + 0.2 = 0.969535971 Simplifying x + 0.2 = 0.969535971 Reorder the terms: 0.2 + x = 0.969535971 Solving 0.2 + x = 0.969535971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 0.969535971 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 0.969535971 + -0.2 x = 0.969535971 + -0.2 Combine like terms: 0.969535971 + -0.2 = 0.769535971 x = 0.769535971 Simplifying x = 0.769535971Subproblem 2
x + 0.2 = -0.969535971 Simplifying x + 0.2 = -0.969535971 Reorder the terms: 0.2 + x = -0.969535971 Solving 0.2 + x = -0.969535971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -0.969535971 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -0.969535971 + -0.2 x = -0.969535971 + -0.2 Combine like terms: -0.969535971 + -0.2 = -1.169535971 x = -1.169535971 Simplifying x = -1.169535971Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.769535971, -1.169535971}
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