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Simplifying 5x(2x + 7) = 2 Reorder the terms: 5x(7 + 2x) = 2 (7 * 5x + 2x * 5x) = 2 (35x + 10x2) = 2 Solving 35x + 10x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + 35x + 10x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 35x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.2 + 3.5x + x2 = 0.0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 3.5x + 0.2 + x2 = 0.0 + 0.2 Reorder the terms: -0.2 + 0.2 + 3.5x + x2 = 0.0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 3.5x + x2 = 0.0 + 0.2 3.5x + x2 = 0.0 + 0.2 Combine like terms: 0.0 + 0.2 = 0.2 3.5x + x2 = 0.2 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 0.2 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 0.2 + 3.0625 Combine like terms: 0.2 + 3.0625 = 3.2625 3.0625 + 3.5x + x2 = 3.2625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 3.2625 Calculate the square root of the right side: 1.806239187 Break this problem into two subproblems by setting (x + 1.75) equal to 1.806239187 and -1.806239187.Subproblem 1
x + 1.75 = 1.806239187 Simplifying x + 1.75 = 1.806239187 Reorder the terms: 1.75 + x = 1.806239187 Solving 1.75 + x = 1.806239187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 1.806239187 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 1.806239187 + -1.75 x = 1.806239187 + -1.75 Combine like terms: 1.806239187 + -1.75 = 0.056239187 x = 0.056239187 Simplifying x = 0.056239187Subproblem 2
x + 1.75 = -1.806239187 Simplifying x + 1.75 = -1.806239187 Reorder the terms: 1.75 + x = -1.806239187 Solving 1.75 + x = -1.806239187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -1.806239187 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -1.806239187 + -1.75 x = -1.806239187 + -1.75 Combine like terms: -1.806239187 + -1.75 = -3.556239187 x = -3.556239187 Simplifying x = -3.556239187Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.056239187, -3.556239187}
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