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Simplifying 5x2 + 2x + -35 = 0 Reorder the terms: -35 + 2x + 5x2 = 0 Solving -35 + 2x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7 + 0.4x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 0.4x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 0.4x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 0.4x + x2 = 0 + 7 0.4x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 0.4x + x2 = 7 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 = 7 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 7 + 0.04 Combine like terms: 7 + 0.04 = 7.04 0.04 + 0.4x + x2 = 7.04 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 7.04 Calculate the square root of the right side: 2.653299832 Break this problem into two subproblems by setting (x + 0.2) equal to 2.653299832 and -2.653299832.Subproblem 1
x + 0.2 = 2.653299832 Simplifying x + 0.2 = 2.653299832 Reorder the terms: 0.2 + x = 2.653299832 Solving 0.2 + x = 2.653299832 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 = 2.653299832 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 2.653299832 + -0.2 x = 2.653299832 + -0.2 Combine like terms: 2.653299832 + -0.2 = 2.453299832 x = 2.453299832 Simplifying x = 2.453299832Subproblem 2
x + 0.2 = -2.653299832 Simplifying x + 0.2 = -2.653299832 Reorder the terms: 0.2 + x = -2.653299832 Solving 0.2 + x = -2.653299832 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 = -2.653299832 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -2.653299832 + -0.2 x = -2.653299832 + -0.2 Combine like terms: -2.653299832 + -0.2 = -2.853299832 x = -2.853299832 Simplifying x = -2.853299832Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.453299832, -2.853299832}
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