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Simplifying 7x(x + -3) = 2x + 19 Reorder the terms: 7x(-3 + x) = 2x + 19 (-3 * 7x + x * 7x) = 2x + 19 (-21x + 7x2) = 2x + 19 Reorder the terms: -21x + 7x2 = 19 + 2x Solving -21x + 7x2 = 19 + 2x Solving for variable 'x'. Reorder the terms: -19 + -21x + -2x + 7x2 = 19 + 2x + -19 + -2x Combine like terms: -21x + -2x = -23x -19 + -23x + 7x2 = 19 + 2x + -19 + -2x Reorder the terms: -19 + -23x + 7x2 = 19 + -19 + 2x + -2x Combine like terms: 19 + -19 = 0 -19 + -23x + 7x2 = 0 + 2x + -2x -19 + -23x + 7x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -19 + -23x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.714285714 + -3.285714286x + x2 = 0 Move the constant term to the right: Add '2.714285714' to each side of the equation. -2.714285714 + -3.285714286x + 2.714285714 + x2 = 0 + 2.714285714 Reorder the terms: -2.714285714 + 2.714285714 + -3.285714286x + x2 = 0 + 2.714285714 Combine like terms: -2.714285714 + 2.714285714 = 0.000000000 0.000000000 + -3.285714286x + x2 = 0 + 2.714285714 -3.285714286x + x2 = 0 + 2.714285714 Combine like terms: 0 + 2.714285714 = 2.714285714 -3.285714286x + x2 = 2.714285714 The x term is -3.285714286x. Take half its coefficient (-1.642857143). Square it (2.698979592) and add it to both sides. Add '2.698979592' to each side of the equation. -3.285714286x + 2.698979592 + x2 = 2.714285714 + 2.698979592 Reorder the terms: 2.698979592 + -3.285714286x + x2 = 2.714285714 + 2.698979592 Combine like terms: 2.714285714 + 2.698979592 = 5.413265306 2.698979592 + -3.285714286x + x2 = 5.413265306 Factor a perfect square on the left side: (x + -1.642857143)(x + -1.642857143) = 5.413265306 Calculate the square root of the right side: 2.326642496 Break this problem into two subproblems by setting (x + -1.642857143) equal to 2.326642496 and -2.326642496.Subproblem 1
x + -1.642857143 = 2.326642496 Simplifying x + -1.642857143 = 2.326642496 Reorder the terms: -1.642857143 + x = 2.326642496 Solving -1.642857143 + x = 2.326642496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.642857143' to each side of the equation. -1.642857143 + 1.642857143 + x = 2.326642496 + 1.642857143 Combine like terms: -1.642857143 + 1.642857143 = 0.000000000 0.000000000 + x = 2.326642496 + 1.642857143 x = 2.326642496 + 1.642857143 Combine like terms: 2.326642496 + 1.642857143 = 3.969499639 x = 3.969499639 Simplifying x = 3.969499639Subproblem 2
x + -1.642857143 = -2.326642496 Simplifying x + -1.642857143 = -2.326642496 Reorder the terms: -1.642857143 + x = -2.326642496 Solving -1.642857143 + x = -2.326642496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.642857143' to each side of the equation. -1.642857143 + 1.642857143 + x = -2.326642496 + 1.642857143 Combine like terms: -1.642857143 + 1.642857143 = 0.000000000 0.000000000 + x = -2.326642496 + 1.642857143 x = -2.326642496 + 1.642857143 Combine like terms: -2.326642496 + 1.642857143 = -0.683785353 x = -0.683785353 Simplifying x = -0.683785353Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.969499639, -0.683785353}
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