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Simplifying 9x2 + -4x = 1 Reorder the terms: -4x + 9x2 = 1 Solving -4x + 9x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + -4x + 9x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -4x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.1111111111 + -0.4444444444x + x2 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + -0.4444444444x + 0.1111111111 + x2 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + -0.4444444444x + x2 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + -0.4444444444x + x2 = 0 + 0.1111111111 -0.4444444444x + x2 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 -0.4444444444x + x2 = 0.1111111111 The x term is -0.4444444444x. Take half its coefficient (-0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. -0.4444444444x + 0.04938271604 + x2 = 0.1111111111 + 0.04938271604 Reorder the terms: 0.04938271604 + -0.4444444444x + x2 = 0.1111111111 + 0.04938271604 Combine like terms: 0.1111111111 + 0.04938271604 = 0.16049382714 0.04938271604 + -0.4444444444x + x2 = 0.16049382714 Factor a perfect square on the left side: (x + -0.2222222222)(x + -0.2222222222) = 0.16049382714 Calculate the square root of the right side: 0.400616808 Break this problem into two subproblems by setting (x + -0.2222222222) equal to 0.400616808 and -0.400616808.Subproblem 1
x + -0.2222222222 = 0.400616808 Simplifying x + -0.2222222222 = 0.400616808 Reorder the terms: -0.2222222222 + x = 0.400616808 Solving -0.2222222222 + x = 0.400616808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + x = 0.400616808 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = 0.400616808 + 0.2222222222 x = 0.400616808 + 0.2222222222 Combine like terms: 0.400616808 + 0.2222222222 = 0.6228390302 x = 0.6228390302 Simplifying x = 0.6228390302Subproblem 2
x + -0.2222222222 = -0.400616808 Simplifying x + -0.2222222222 = -0.400616808 Reorder the terms: -0.2222222222 + x = -0.400616808 Solving -0.2222222222 + x = -0.400616808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + x = -0.400616808 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = -0.400616808 + 0.2222222222 x = -0.400616808 + 0.2222222222 Combine like terms: -0.400616808 + 0.2222222222 = -0.1783945858 x = -0.1783945858 Simplifying x = -0.1783945858Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6228390302, -0.1783945858}
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