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Simplifying 4x(5x + -3) + -15 = 0 Reorder the terms: 4x(-3 + 5x) + -15 = 0 (-3 * 4x + 5x * 4x) + -15 = 0 (-12x + 20x2) + -15 = 0 Reorder the terms: -15 + -12x + 20x2 = 0 Solving -15 + -12x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.75 + -0.6x + x2 = 0.0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -0.6x + 0.75 + x2 = 0.0 + 0.75 Reorder the terms: -0.75 + 0.75 + -0.6x + x2 = 0.0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -0.6x + x2 = 0.0 + 0.75 -0.6x + x2 = 0.0 + 0.75 Combine like terms: 0.0 + 0.75 = 0.75 -0.6x + x2 = 0.75 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 0.75 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 0.75 + 0.09 Combine like terms: 0.75 + 0.09 = 0.84 0.09 + -0.6x + x2 = 0.84 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 0.84 Calculate the square root of the right side: 0.916515139 Break this problem into two subproblems by setting (x + -0.3) equal to 0.916515139 and -0.916515139.Subproblem 1
x + -0.3 = 0.916515139 Simplifying x + -0.3 = 0.916515139 Reorder the terms: -0.3 + x = 0.916515139 Solving -0.3 + x = 0.916515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 0.916515139 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 0.916515139 + 0.3 x = 0.916515139 + 0.3 Combine like terms: 0.916515139 + 0.3 = 1.216515139 x = 1.216515139 Simplifying x = 1.216515139Subproblem 2
x + -0.3 = -0.916515139 Simplifying x + -0.3 = -0.916515139 Reorder the terms: -0.3 + x = -0.916515139 Solving -0.3 + x = -0.916515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -0.916515139 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -0.916515139 + 0.3 x = -0.916515139 + 0.3 Combine like terms: -0.916515139 + 0.3 = -0.616515139 x = -0.616515139 Simplifying x = -0.616515139Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.216515139, -0.616515139}
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