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Simplifying 340 = (2x + 3) * x Reorder the terms: 340 = (3 + 2x) * x Reorder the terms for easier multiplication: 340 = x(3 + 2x) 340 = (3 * x + 2x * x) 340 = (3x + 2x2) Solving 340 = 3x + 2x2 Solving for variable 'x'. Reorder the terms: 340 + -3x + -2x2 = 3x + -3x + 2x2 + -2x2 Combine like terms: 3x + -3x = 0 340 + -3x + -2x2 = 0 + 2x2 + -2x2 340 + -3x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 340 + -3x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -170 + 1.5x + x2 = 0 Move the constant term to the right: Add '170' to each side of the equation. -170 + 1.5x + 170 + x2 = 0 + 170 Reorder the terms: -170 + 170 + 1.5x + x2 = 0 + 170 Combine like terms: -170 + 170 = 0 0 + 1.5x + x2 = 0 + 170 1.5x + x2 = 0 + 170 Combine like terms: 0 + 170 = 170 1.5x + x2 = 170 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 170 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 170 + 0.5625 Combine like terms: 170 + 0.5625 = 170.5625 0.5625 + 1.5x + x2 = 170.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 170.5625 Calculate the square root of the right side: 13.059957887 Break this problem into two subproblems by setting (x + 0.75) equal to 13.059957887 and -13.059957887.Subproblem 1
x + 0.75 = 13.059957887 Simplifying x + 0.75 = 13.059957887 Reorder the terms: 0.75 + x = 13.059957887 Solving 0.75 + x = 13.059957887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 13.059957887 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 13.059957887 + -0.75 x = 13.059957887 + -0.75 Combine like terms: 13.059957887 + -0.75 = 12.309957887 x = 12.309957887 Simplifying x = 12.309957887Subproblem 2
x + 0.75 = -13.059957887 Simplifying x + 0.75 = -13.059957887 Reorder the terms: 0.75 + x = -13.059957887 Solving 0.75 + x = -13.059957887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -13.059957887 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -13.059957887 + -0.75 x = -13.059957887 + -0.75 Combine like terms: -13.059957887 + -0.75 = -13.809957887 x = -13.809957887 Simplifying x = -13.809957887Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.309957887, -13.809957887}
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