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Simplifying 5x2 + 2x = 175 Reorder the terms: 2x + 5x2 = 175 Solving 2x + 5x2 = 175 Solving for variable 'x'. Reorder the terms: -175 + 2x + 5x2 = 175 + -175 Combine like terms: 175 + -175 = 0 -175 + 2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -35 + 0.4x + x2 = 0 Move the constant term to the right: Add '35' to each side of the equation. -35 + 0.4x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + 0.4x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 0.4x + x2 = 0 + 35 0.4x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 0.4x + x2 = 35 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 = 35 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 35 + 0.04 Combine like terms: 35 + 0.04 = 35.04 0.04 + 0.4x + x2 = 35.04 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 35.04 Calculate the square root of the right side: 5.919459435 Break this problem into two subproblems by setting (x + 0.2) equal to 5.919459435 and -5.919459435.Subproblem 1
x + 0.2 = 5.919459435 Simplifying x + 0.2 = 5.919459435 Reorder the terms: 0.2 + x = 5.919459435 Solving 0.2 + x = 5.919459435 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 = 5.919459435 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 5.919459435 + -0.2 x = 5.919459435 + -0.2 Combine like terms: 5.919459435 + -0.2 = 5.719459435 x = 5.719459435 Simplifying x = 5.719459435Subproblem 2
x + 0.2 = -5.919459435 Simplifying x + 0.2 = -5.919459435 Reorder the terms: 0.2 + x = -5.919459435 Solving 0.2 + x = -5.919459435 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 = -5.919459435 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -5.919459435 + -0.2 x = -5.919459435 + -0.2 Combine like terms: -5.919459435 + -0.2 = -6.119459435 x = -6.119459435 Simplifying x = -6.119459435Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.719459435, -6.119459435}
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