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Simplifying 3x2 + 21x + -7.5 = 0 Reorder the terms: -7.5 + 21x + 3x2 = 0 Solving -7.5 + 21x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.5 + 7x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 7x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 7x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 7x + x2 = 0 + 2.5 7x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 7x + x2 = 2.5 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 2.5 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 2.5 + 12.25 Combine like terms: 2.5 + 12.25 = 14.75 12.25 + 7x + x2 = 14.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 14.75 Calculate the square root of the right side: 3.840572874 Break this problem into two subproblems by setting (x + 3.5) equal to 3.840572874 and -3.840572874.Subproblem 1
x + 3.5 = 3.840572874 Simplifying x + 3.5 = 3.840572874 Reorder the terms: 3.5 + x = 3.840572874 Solving 3.5 + x = 3.840572874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 3.840572874 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.840572874 + -3.5 x = 3.840572874 + -3.5 Combine like terms: 3.840572874 + -3.5 = 0.340572874 x = 0.340572874 Simplifying x = 0.340572874Subproblem 2
x + 3.5 = -3.840572874 Simplifying x + 3.5 = -3.840572874 Reorder the terms: 3.5 + x = -3.840572874 Solving 3.5 + x = -3.840572874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -3.840572874 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.840572874 + -3.5 x = -3.840572874 + -3.5 Combine like terms: -3.840572874 + -3.5 = -7.340572874 x = -7.340572874 Simplifying x = -7.340572874Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.340572874, -7.340572874}
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