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Simplifying 3x(2x + -5) = 7 Reorder the terms: 3x(-5 + 2x) = 7 (-5 * 3x + 2x * 3x) = 7 (-15x + 6x2) = 7 Solving -15x + 6x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + -15x + 6x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -15x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.166666667 + -2.5x + x2 = 0 Move the constant term to the right: Add '1.166666667' to each side of the equation. -1.166666667 + -2.5x + 1.166666667 + x2 = 0 + 1.166666667 Reorder the terms: -1.166666667 + 1.166666667 + -2.5x + x2 = 0 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + -2.5x + x2 = 0 + 1.166666667 -2.5x + x2 = 0 + 1.166666667 Combine like terms: 0 + 1.166666667 = 1.166666667 -2.5x + x2 = 1.166666667 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 1.166666667 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 1.166666667 + 1.5625 Combine like terms: 1.166666667 + 1.5625 = 2.729166667 1.5625 + -2.5x + x2 = 2.729166667 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 2.729166667 Calculate the square root of the right side: 1.652018967 Break this problem into two subproblems by setting (x + -1.25) equal to 1.652018967 and -1.652018967.Subproblem 1
x + -1.25 = 1.652018967 Simplifying x + -1.25 = 1.652018967 Reorder the terms: -1.25 + x = 1.652018967 Solving -1.25 + x = 1.652018967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 1.652018967 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 1.652018967 + 1.25 x = 1.652018967 + 1.25 Combine like terms: 1.652018967 + 1.25 = 2.902018967 x = 2.902018967 Simplifying x = 2.902018967Subproblem 2
x + -1.25 = -1.652018967 Simplifying x + -1.25 = -1.652018967 Reorder the terms: -1.25 + x = -1.652018967 Solving -1.25 + x = -1.652018967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -1.652018967 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -1.652018967 + 1.25 x = -1.652018967 + 1.25 Combine like terms: -1.652018967 + 1.25 = -0.402018967 x = -0.402018967 Simplifying x = -0.402018967Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.902018967, -0.402018967}
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