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Simplifying -2.2x(x + 1) = 0.3(x + -1.5) Reorder the terms: -2.2x(1 + x) = 0.3(x + -1.5) (1 * -2.2x + x * -2.2x) = 0.3(x + -1.5) (-2.2x + -2.2x2) = 0.3(x + -1.5) Reorder the terms: -2.2x + -2.2x2 = 0.3(-1.5 + x) -2.2x + -2.2x2 = (-1.5 * 0.3 + x * 0.3) -2.2x + -2.2x2 = (-0.45 + 0.3x) Solving -2.2x + -2.2x2 = -0.45 + 0.3x Solving for variable 'x'. Reorder the terms: 0.45 + -2.2x + -0.3x + -2.2x2 = -0.45 + 0.3x + 0.45 + -0.3x Combine like terms: -2.2x + -0.3x = -2.5x 0.45 + -2.5x + -2.2x2 = -0.45 + 0.3x + 0.45 + -0.3x Reorder the terms: 0.45 + -2.5x + -2.2x2 = -0.45 + 0.45 + 0.3x + -0.3x Combine like terms: -0.45 + 0.45 = 0.00 0.45 + -2.5x + -2.2x2 = 0.00 + 0.3x + -0.3x 0.45 + -2.5x + -2.2x2 = 0.3x + -0.3x Combine like terms: 0.3x + -0.3x = 0.0 0.45 + -2.5x + -2.2x2 = 0.0 Begin completing the square. Divide all terms by -2.2 the coefficient of the squared term: Divide each side by '-2.2'. -0.2045454545 + 1.136363636x + x2 = 0 Move the constant term to the right: Add '0.2045454545' to each side of the equation. -0.2045454545 + 1.136363636x + 0.2045454545 + x2 = 0 + 0.2045454545 Reorder the terms: -0.2045454545 + 0.2045454545 + 1.136363636x + x2 = 0 + 0.2045454545 Combine like terms: -0.2045454545 + 0.2045454545 = 0.0000000000 0.0000000000 + 1.136363636x + x2 = 0 + 0.2045454545 1.136363636x + x2 = 0 + 0.2045454545 Combine like terms: 0 + 0.2045454545 = 0.2045454545 1.136363636x + x2 = 0.2045454545 The x term is 1.136363636x. Take half its coefficient (0.568181818). Square it (0.3228305783) and add it to both sides. Add '0.3228305783' to each side of the equation. 1.136363636x + 0.3228305783 + x2 = 0.2045454545 + 0.3228305783 Reorder the terms: 0.3228305783 + 1.136363636x + x2 = 0.2045454545 + 0.3228305783 Combine like terms: 0.2045454545 + 0.3228305783 = 0.5273760328 0.3228305783 + 1.136363636x + x2 = 0.5273760328 Factor a perfect square on the left side: (x + 0.568181818)(x + 0.568181818) = 0.5273760328 Calculate the square root of the right side: 0.726206605 Break this problem into two subproblems by setting (x + 0.568181818) equal to 0.726206605 and -0.726206605.Subproblem 1
x + 0.568181818 = 0.726206605 Simplifying x + 0.568181818 = 0.726206605 Reorder the terms: 0.568181818 + x = 0.726206605 Solving 0.568181818 + x = 0.726206605 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.568181818' to each side of the equation. 0.568181818 + -0.568181818 + x = 0.726206605 + -0.568181818 Combine like terms: 0.568181818 + -0.568181818 = 0.000000000 0.000000000 + x = 0.726206605 + -0.568181818 x = 0.726206605 + -0.568181818 Combine like terms: 0.726206605 + -0.568181818 = 0.158024787 x = 0.158024787 Simplifying x = 0.158024787Subproblem 2
x + 0.568181818 = -0.726206605 Simplifying x + 0.568181818 = -0.726206605 Reorder the terms: 0.568181818 + x = -0.726206605 Solving 0.568181818 + x = -0.726206605 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.568181818' to each side of the equation. 0.568181818 + -0.568181818 + x = -0.726206605 + -0.568181818 Combine like terms: 0.568181818 + -0.568181818 = 0.000000000 0.000000000 + x = -0.726206605 + -0.568181818 x = -0.726206605 + -0.568181818 Combine like terms: -0.726206605 + -0.568181818 = -1.294388423 x = -1.294388423 Simplifying x = -1.294388423Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.158024787, -1.294388423}
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