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Simplifying 3x(2x + -5) = 7 + -3x Reorder the terms: 3x(-5 + 2x) = 7 + -3x (-5 * 3x + 2x * 3x) = 7 + -3x (-15x + 6x2) = 7 + -3x Solving -15x + 6x2 = 7 + -3x Solving for variable 'x'. Reorder the terms: -7 + -15x + 3x + 6x2 = 7 + -3x + -7 + 3x Combine like terms: -15x + 3x = -12x -7 + -12x + 6x2 = 7 + -3x + -7 + 3x Reorder the terms: -7 + -12x + 6x2 = 7 + -7 + -3x + 3x Combine like terms: 7 + -7 = 0 -7 + -12x + 6x2 = 0 + -3x + 3x -7 + -12x + 6x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -7 + -12x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.166666667 + -2x + x2 = 0 Move the constant term to the right: Add '1.166666667' to each side of the equation. -1.166666667 + -2x + 1.166666667 + x2 = 0 + 1.166666667 Reorder the terms: -1.166666667 + 1.166666667 + -2x + x2 = 0 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + -2x + x2 = 0 + 1.166666667 -2x + x2 = 0 + 1.166666667 Combine like terms: 0 + 1.166666667 = 1.166666667 -2x + x2 = 1.166666667 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 1.166666667 + 1 Reorder the terms: 1 + -2x + x2 = 1.166666667 + 1 Combine like terms: 1.166666667 + 1 = 2.166666667 1 + -2x + x2 = 2.166666667 Factor a perfect square on the left side: (x + -1)(x + -1) = 2.166666667 Calculate the square root of the right side: 1.471960145 Break this problem into two subproblems by setting (x + -1) equal to 1.471960145 and -1.471960145.Subproblem 1
x + -1 = 1.471960145 Simplifying x + -1 = 1.471960145 Reorder the terms: -1 + x = 1.471960145 Solving -1 + x = 1.471960145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.471960145 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.471960145 + 1 x = 1.471960145 + 1 Combine like terms: 1.471960145 + 1 = 2.471960145 x = 2.471960145 Simplifying x = 2.471960145Subproblem 2
x + -1 = -1.471960145 Simplifying x + -1 = -1.471960145 Reorder the terms: -1 + x = -1.471960145 Solving -1 + x = -1.471960145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.471960145 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.471960145 + 1 x = -1.471960145 + 1 Combine like terms: -1.471960145 + 1 = -0.471960145 x = -0.471960145 Simplifying x = -0.471960145Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.471960145, -0.471960145}
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