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Simplifying 7x(x + -4) + 3 = 5x + -9 Reorder the terms: 7x(-4 + x) + 3 = 5x + -9 (-4 * 7x + x * 7x) + 3 = 5x + -9 (-28x + 7x2) + 3 = 5x + -9 Reorder the terms: 3 + -28x + 7x2 = 5x + -9 Reorder the terms: 3 + -28x + 7x2 = -9 + 5x Solving 3 + -28x + 7x2 = -9 + 5x Solving for variable 'x'. Reorder the terms: 3 + 9 + -28x + -5x + 7x2 = -9 + 5x + 9 + -5x Combine like terms: 3 + 9 = 12 12 + -28x + -5x + 7x2 = -9 + 5x + 9 + -5x Combine like terms: -28x + -5x = -33x 12 + -33x + 7x2 = -9 + 5x + 9 + -5x Reorder the terms: 12 + -33x + 7x2 = -9 + 9 + 5x + -5x Combine like terms: -9 + 9 = 0 12 + -33x + 7x2 = 0 + 5x + -5x 12 + -33x + 7x2 = 5x + -5x Combine like terms: 5x + -5x = 0 12 + -33x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1.714285714 + -4.714285714x + x2 = 0 Move the constant term to the right: Add '-1.714285714' to each side of the equation. 1.714285714 + -4.714285714x + -1.714285714 + x2 = 0 + -1.714285714 Reorder the terms: 1.714285714 + -1.714285714 + -4.714285714x + x2 = 0 + -1.714285714 Combine like terms: 1.714285714 + -1.714285714 = 0.000000000 0.000000000 + -4.714285714x + x2 = 0 + -1.714285714 -4.714285714x + x2 = 0 + -1.714285714 Combine like terms: 0 + -1.714285714 = -1.714285714 -4.714285714x + x2 = -1.714285714 The x term is -4.714285714x. Take half its coefficient (-2.357142857). Square it (5.556122448) and add it to both sides. Add '5.556122448' to each side of the equation. -4.714285714x + 5.556122448 + x2 = -1.714285714 + 5.556122448 Reorder the terms: 5.556122448 + -4.714285714x + x2 = -1.714285714 + 5.556122448 Combine like terms: -1.714285714 + 5.556122448 = 3.841836734 5.556122448 + -4.714285714x + x2 = 3.841836734 Factor a perfect square on the left side: (x + -2.357142857)(x + -2.357142857) = 3.841836734 Calculate the square root of the right side: 1.96006039 Break this problem into two subproblems by setting (x + -2.357142857) equal to 1.96006039 and -1.96006039.Subproblem 1
x + -2.357142857 = 1.96006039 Simplifying x + -2.357142857 = 1.96006039 Reorder the terms: -2.357142857 + x = 1.96006039 Solving -2.357142857 + x = 1.96006039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.357142857' to each side of the equation. -2.357142857 + 2.357142857 + x = 1.96006039 + 2.357142857 Combine like terms: -2.357142857 + 2.357142857 = 0.000000000 0.000000000 + x = 1.96006039 + 2.357142857 x = 1.96006039 + 2.357142857 Combine like terms: 1.96006039 + 2.357142857 = 4.317203247 x = 4.317203247 Simplifying x = 4.317203247Subproblem 2
x + -2.357142857 = -1.96006039 Simplifying x + -2.357142857 = -1.96006039 Reorder the terms: -2.357142857 + x = -1.96006039 Solving -2.357142857 + x = -1.96006039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.357142857' to each side of the equation. -2.357142857 + 2.357142857 + x = -1.96006039 + 2.357142857 Combine like terms: -2.357142857 + 2.357142857 = 0.000000000 0.000000000 + x = -1.96006039 + 2.357142857 x = -1.96006039 + 2.357142857 Combine like terms: -1.96006039 + 2.357142857 = 0.397082467 x = 0.397082467 Simplifying x = 0.397082467Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.317203247, 0.397082467}
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