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Simplifying 5x2 + 75x + 1 = 0 Reorder the terms: 1 + 75x + 5x2 = 0 Solving 1 + 75x + 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'. 0.2 + 15x + x2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + 15x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + 15x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + 15x + x2 = 0 + -0.2 15x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 15x + x2 = -0.2 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = -0.2 + 56.25 Reorder the terms: 56.25 + 15x + x2 = -0.2 + 56.25 Combine like terms: -0.2 + 56.25 = 56.05 56.25 + 15x + x2 = 56.05 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 56.05 Calculate the square root of the right side: 7.486654794 Break this problem into two subproblems by setting (x + 7.5) equal to 7.486654794 and -7.486654794.Subproblem 1
x + 7.5 = 7.486654794 Simplifying x + 7.5 = 7.486654794 Reorder the terms: 7.5 + x = 7.486654794 Solving 7.5 + x = 7.486654794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 7.486654794 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 7.486654794 + -7.5 x = 7.486654794 + -7.5 Combine like terms: 7.486654794 + -7.5 = -0.013345206 x = -0.013345206 Simplifying x = -0.013345206Subproblem 2
x + 7.5 = -7.486654794 Simplifying x + 7.5 = -7.486654794 Reorder the terms: 7.5 + x = -7.486654794 Solving 7.5 + x = -7.486654794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -7.486654794 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -7.486654794 + -7.5 x = -7.486654794 + -7.5 Combine like terms: -7.486654794 + -7.5 = -14.986654794 x = -14.986654794 Simplifying x = -14.986654794Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.013345206, -14.986654794}
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