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Simplifying 3x(2x + -7) = 5 Reorder the terms: 3x(-7 + 2x) = 5 (-7 * 3x + 2x * 3x) = 5 (-21x + 6x2) = 5 Solving -21x + 6x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + -21x + 6x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -21x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.8333333333 + -3.5x + x2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + -3.5x + 0.8333333333 + x2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + -3.5x + x2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + -3.5x + x2 = 0 + 0.8333333333 -3.5x + x2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 -3.5x + x2 = 0.8333333333 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 = 0.8333333333 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 0.8333333333 + 3.0625 Combine like terms: 0.8333333333 + 3.0625 = 3.8958333333 3.0625 + -3.5x + x2 = 3.8958333333 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 3.8958333333 Calculate the square root of the right side: 1.973786547 Break this problem into two subproblems by setting (x + -1.75) equal to 1.973786547 and -1.973786547.Subproblem 1
x + -1.75 = 1.973786547 Simplifying x + -1.75 = 1.973786547 Reorder the terms: -1.75 + x = 1.973786547 Solving -1.75 + x = 1.973786547 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 = 1.973786547 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 1.973786547 + 1.75 x = 1.973786547 + 1.75 Combine like terms: 1.973786547 + 1.75 = 3.723786547 x = 3.723786547 Simplifying x = 3.723786547Subproblem 2
x + -1.75 = -1.973786547 Simplifying x + -1.75 = -1.973786547 Reorder the terms: -1.75 + x = -1.973786547 Solving -1.75 + x = -1.973786547 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 = -1.973786547 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -1.973786547 + 1.75 x = -1.973786547 + 1.75 Combine like terms: -1.973786547 + 1.75 = -0.223786547 x = -0.223786547 Simplifying x = -0.223786547Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.723786547, -0.223786547}
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