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Simplifying 30 = 2x2 + 7x + -5 Reorder the terms: 30 = -5 + 7x + 2x2 Solving 30 = -5 + 7x + 2x2 Solving for variable 'x'. Combine like terms: 30 + 5 = 35 35 + -7x + -2x2 = -5 + 7x + 2x2 + 5 + -7x + -2x2 Reorder the terms: 35 + -7x + -2x2 = -5 + 5 + 7x + -7x + 2x2 + -2x2 Combine like terms: -5 + 5 = 0 35 + -7x + -2x2 = 0 + 7x + -7x + 2x2 + -2x2 35 + -7x + -2x2 = 7x + -7x + 2x2 + -2x2 Combine like terms: 7x + -7x = 0 35 + -7x + -2x2 = 0 + 2x2 + -2x2 35 + -7x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 35 + -7x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -17.5 + 3.5x + x2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + 3.5x + 17.5 + x2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + 3.5x + x2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + 3.5x + x2 = 0 + 17.5 3.5x + x2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 3.5x + x2 = 17.5 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 = 17.5 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 17.5 + 3.0625 Combine like terms: 17.5 + 3.0625 = 20.5625 3.0625 + 3.5x + x2 = 20.5625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 20.5625 Calculate the square root of the right side: 4.534589287 Break this problem into two subproblems by setting (x + 1.75) equal to 4.534589287 and -4.534589287.Subproblem 1
x + 1.75 = 4.534589287 Simplifying x + 1.75 = 4.534589287 Reorder the terms: 1.75 + x = 4.534589287 Solving 1.75 + x = 4.534589287 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 = 4.534589287 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 4.534589287 + -1.75 x = 4.534589287 + -1.75 Combine like terms: 4.534589287 + -1.75 = 2.784589287 x = 2.784589287 Simplifying x = 2.784589287Subproblem 2
x + 1.75 = -4.534589287 Simplifying x + 1.75 = -4.534589287 Reorder the terms: 1.75 + x = -4.534589287 Solving 1.75 + x = -4.534589287 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 = -4.534589287 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -4.534589287 + -1.75 x = -4.534589287 + -1.75 Combine like terms: -4.534589287 + -1.75 = -6.284589287 x = -6.284589287 Simplifying x = -6.284589287Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.784589287, -6.284589287}
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