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Simplifying 3x(2x + -5) = 2(3x + -2) Reorder the terms: 3x(-5 + 2x) = 2(3x + -2) (-5 * 3x + 2x * 3x) = 2(3x + -2) (-15x + 6x2) = 2(3x + -2) Reorder the terms: -15x + 6x2 = 2(-2 + 3x) -15x + 6x2 = (-2 * 2 + 3x * 2) -15x + 6x2 = (-4 + 6x) Solving -15x + 6x2 = -4 + 6x Solving for variable 'x'. Reorder the terms: 4 + -15x + -6x + 6x2 = -4 + 6x + 4 + -6x Combine like terms: -15x + -6x = -21x 4 + -21x + 6x2 = -4 + 6x + 4 + -6x Reorder the terms: 4 + -21x + 6x2 = -4 + 4 + 6x + -6x Combine like terms: -4 + 4 = 0 4 + -21x + 6x2 = 0 + 6x + -6x 4 + -21x + 6x2 = 6x + -6x Combine like terms: 6x + -6x = 0 4 + -21x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.6666666667 + -3.5x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -3.5x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -3.5x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -3.5x + x2 = 0 + -0.6666666667 -3.5x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -3.5x + x2 = -0.6666666667 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 = -0.6666666667 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = -0.6666666667 + 3.0625 Combine like terms: -0.6666666667 + 3.0625 = 2.3958333333 3.0625 + -3.5x + x2 = 2.3958333333 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 2.3958333333 Calculate the square root of the right side: 1.547847968 Break this problem into two subproblems by setting (x + -1.75) equal to 1.547847968 and -1.547847968.Subproblem 1
x + -1.75 = 1.547847968 Simplifying x + -1.75 = 1.547847968 Reorder the terms: -1.75 + x = 1.547847968 Solving -1.75 + x = 1.547847968 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 = 1.547847968 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 1.547847968 + 1.75 x = 1.547847968 + 1.75 Combine like terms: 1.547847968 + 1.75 = 3.297847968 x = 3.297847968 Simplifying x = 3.297847968Subproblem 2
x + -1.75 = -1.547847968 Simplifying x + -1.75 = -1.547847968 Reorder the terms: -1.75 + x = -1.547847968 Solving -1.75 + x = -1.547847968 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 = -1.547847968 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -1.547847968 + 1.75 x = -1.547847968 + 1.75 Combine like terms: -1.547847968 + 1.75 = 0.202152032 x = 0.202152032 Simplifying x = 0.202152032Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.297847968, 0.202152032}
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