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Simplifying 0.4x(x + -9) = 0.3(x + 4) Reorder the terms: 0.4x(-9 + x) = 0.3(x + 4) (-9 * 0.4x + x * 0.4x) = 0.3(x + 4) (-3.6x + 0.4x2) = 0.3(x + 4) Reorder the terms: -3.6x + 0.4x2 = 0.3(4 + x) -3.6x + 0.4x2 = (4 * 0.3 + x * 0.3) -3.6x + 0.4x2 = (1.2 + 0.3x) Solving -3.6x + 0.4x2 = 1.2 + 0.3x Solving for variable 'x'. Reorder the terms: -1.2 + -3.6x + -0.3x + 0.4x2 = 1.2 + 0.3x + -1.2 + -0.3x Combine like terms: -3.6x + -0.3x = -3.9x -1.2 + -3.9x + 0.4x2 = 1.2 + 0.3x + -1.2 + -0.3x Reorder the terms: -1.2 + -3.9x + 0.4x2 = 1.2 + -1.2 + 0.3x + -0.3x Combine like terms: 1.2 + -1.2 = 0.0 -1.2 + -3.9x + 0.4x2 = 0.0 + 0.3x + -0.3x -1.2 + -3.9x + 0.4x2 = 0.3x + -0.3x Combine like terms: 0.3x + -0.3x = 0.0 -1.2 + -3.9x + 0.4x2 = 0.0 Begin completing the square. Divide all terms by 0.4 the coefficient of the squared term: Divide each side by '0.4'. -3 + -9.75x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -9.75x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -9.75x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -9.75x + x2 = 0 + 3 -9.75x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -9.75x + x2 = 3 The x term is -9.75x. Take half its coefficient (-4.875). Square it (23.765625) and add it to both sides. Add '23.765625' to each side of the equation. -9.75x + 23.765625 + x2 = 3 + 23.765625 Reorder the terms: 23.765625 + -9.75x + x2 = 3 + 23.765625 Combine like terms: 3 + 23.765625 = 26.765625 23.765625 + -9.75x + x2 = 26.765625 Factor a perfect square on the left side: (x + -4.875)(x + -4.875) = 26.765625 Calculate the square root of the right side: 5.173550522 Break this problem into two subproblems by setting (x + -4.875) equal to 5.173550522 and -5.173550522.Subproblem 1
x + -4.875 = 5.173550522 Simplifying x + -4.875 = 5.173550522 Reorder the terms: -4.875 + x = 5.173550522 Solving -4.875 + x = 5.173550522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.875' to each side of the equation. -4.875 + 4.875 + x = 5.173550522 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + x = 5.173550522 + 4.875 x = 5.173550522 + 4.875 Combine like terms: 5.173550522 + 4.875 = 10.048550522 x = 10.048550522 Simplifying x = 10.048550522Subproblem 2
x + -4.875 = -5.173550522 Simplifying x + -4.875 = -5.173550522 Reorder the terms: -4.875 + x = -5.173550522 Solving -4.875 + x = -5.173550522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.875' to each side of the equation. -4.875 + 4.875 + x = -5.173550522 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + x = -5.173550522 + 4.875 x = -5.173550522 + 4.875 Combine like terms: -5.173550522 + 4.875 = -0.298550522 x = -0.298550522 Simplifying x = -0.298550522Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.048550522, -0.298550522}
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