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Simplifying 35x2 + 42x + -24 = 0 Reorder the terms: -24 + 42x + 35x2 = 0 Solving -24 + 42x + 35x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -0.6857142857 + 1.2x + x2 = 0 Move the constant term to the right: Add '0.6857142857' to each side of the equation. -0.6857142857 + 1.2x + 0.6857142857 + x2 = 0 + 0.6857142857 Reorder the terms: -0.6857142857 + 0.6857142857 + 1.2x + x2 = 0 + 0.6857142857 Combine like terms: -0.6857142857 + 0.6857142857 = 0.0000000000 0.0000000000 + 1.2x + x2 = 0 + 0.6857142857 1.2x + x2 = 0 + 0.6857142857 Combine like terms: 0 + 0.6857142857 = 0.6857142857 1.2x + x2 = 0.6857142857 The x term is 1.2x. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2x + 0.36 + x2 = 0.6857142857 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = 0.6857142857 + 0.36 Combine like terms: 0.6857142857 + 0.36 = 1.0457142857 0.36 + 1.2x + x2 = 1.0457142857 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 1.0457142857 Calculate the square root of the right side: 1.022601724 Break this problem into two subproblems by setting (x + 0.6) equal to 1.022601724 and -1.022601724.Subproblem 1
x + 0.6 = 1.022601724 Simplifying x + 0.6 = 1.022601724 Reorder the terms: 0.6 + x = 1.022601724 Solving 0.6 + x = 1.022601724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = 1.022601724 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 1.022601724 + -0.6 x = 1.022601724 + -0.6 Combine like terms: 1.022601724 + -0.6 = 0.422601724 x = 0.422601724 Simplifying x = 0.422601724Subproblem 2
x + 0.6 = -1.022601724 Simplifying x + 0.6 = -1.022601724 Reorder the terms: 0.6 + x = -1.022601724 Solving 0.6 + x = -1.022601724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = -1.022601724 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -1.022601724 + -0.6 x = -1.022601724 + -0.6 Combine like terms: -1.022601724 + -0.6 = -1.622601724 x = -1.622601724 Simplifying x = -1.622601724Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.422601724, -1.622601724}
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