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Simplifying 20x2 = 15 + 3x Solving 20x2 = 15 + 3x Solving for variable 'x'. Reorder the terms: -15 + -3x + 20x2 = 15 + 3x + -15 + -3x Reorder the terms: -15 + -3x + 20x2 = 15 + -15 + 3x + -3x Combine like terms: 15 + -15 = 0 -15 + -3x + 20x2 = 0 + 3x + -3x -15 + -3x + 20x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -15 + -3x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.75 + -0.15x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -0.15x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -0.15x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -0.15x + x2 = 0 + 0.75 -0.15x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -0.15x + x2 = 0.75 The x term is -0.15x. Take half its coefficient (-0.075). Square it (0.005625) and add it to both sides. Add '0.005625' to each side of the equation. -0.15x + 0.005625 + x2 = 0.75 + 0.005625 Reorder the terms: 0.005625 + -0.15x + x2 = 0.75 + 0.005625 Combine like terms: 0.75 + 0.005625 = 0.755625 0.005625 + -0.15x + x2 = 0.755625 Factor a perfect square on the left side: (x + -0.075)(x + -0.075) = 0.755625 Calculate the square root of the right side: 0.869266933 Break this problem into two subproblems by setting (x + -0.075) equal to 0.869266933 and -0.869266933.Subproblem 1
x + -0.075 = 0.869266933 Simplifying x + -0.075 = 0.869266933 Reorder the terms: -0.075 + x = 0.869266933 Solving -0.075 + x = 0.869266933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.075' to each side of the equation. -0.075 + 0.075 + x = 0.869266933 + 0.075 Combine like terms: -0.075 + 0.075 = 0.000 0.000 + x = 0.869266933 + 0.075 x = 0.869266933 + 0.075 Combine like terms: 0.869266933 + 0.075 = 0.944266933 x = 0.944266933 Simplifying x = 0.944266933Subproblem 2
x + -0.075 = -0.869266933 Simplifying x + -0.075 = -0.869266933 Reorder the terms: -0.075 + x = -0.869266933 Solving -0.075 + x = -0.869266933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.075' to each side of the equation. -0.075 + 0.075 + x = -0.869266933 + 0.075 Combine like terms: -0.075 + 0.075 = 0.000 0.000 + x = -0.869266933 + 0.075 x = -0.869266933 + 0.075 Combine like terms: -0.869266933 + 0.075 = -0.794266933 x = -0.794266933 Simplifying x = -0.794266933Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.944266933, -0.794266933}
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