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Simplifying 1.5 = 4x + -5x2 + 0.8 Reorder the terms: 1.5 = 0.8 + 4x + -5x2 Solving 1.5 = 0.8 + 4x + -5x2 Solving for variable 'x'. Combine like terms: 1.5 + -0.8 = 0.7 0.7 + -4x + 5x2 = 0.8 + 4x + -5x2 + -0.8 + -4x + 5x2 Reorder the terms: 0.7 + -4x + 5x2 = 0.8 + -0.8 + 4x + -4x + -5x2 + 5x2 Combine like terms: 0.8 + -0.8 = 0.0 0.7 + -4x + 5x2 = 0.0 + 4x + -4x + -5x2 + 5x2 0.7 + -4x + 5x2 = 4x + -4x + -5x2 + 5x2 Combine like terms: 4x + -4x = 0 0.7 + -4x + 5x2 = 0 + -5x2 + 5x2 0.7 + -4x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 0.7 + -4x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.14 + -0.8x + x2 = 0 Move the constant term to the right: Add '-0.14' to each side of the equation. 0.14 + -0.8x + -0.14 + x2 = 0 + -0.14 Reorder the terms: 0.14 + -0.14 + -0.8x + x2 = 0 + -0.14 Combine like terms: 0.14 + -0.14 = 0.00 0.00 + -0.8x + x2 = 0 + -0.14 -0.8x + x2 = 0 + -0.14 Combine like terms: 0 + -0.14 = -0.14 -0.8x + x2 = -0.14 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = -0.14 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = -0.14 + 0.16 Combine like terms: -0.14 + 0.16 = 0.02 0.16 + -0.8x + x2 = 0.02 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 0.02 Calculate the square root of the right side: 0.141421356 Break this problem into two subproblems by setting (x + -0.4) equal to 0.141421356 and -0.141421356.Subproblem 1
x + -0.4 = 0.141421356 Simplifying x + -0.4 = 0.141421356 Reorder the terms: -0.4 + x = 0.141421356 Solving -0.4 + x = 0.141421356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 0.141421356 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 0.141421356 + 0.4 x = 0.141421356 + 0.4 Combine like terms: 0.141421356 + 0.4 = 0.541421356 x = 0.541421356 Simplifying x = 0.541421356Subproblem 2
x + -0.4 = -0.141421356 Simplifying x + -0.4 = -0.141421356 Reorder the terms: -0.4 + x = -0.141421356 Solving -0.4 + x = -0.141421356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -0.141421356 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -0.141421356 + 0.4 x = -0.141421356 + 0.4 Combine like terms: -0.141421356 + 0.4 = 0.258578644 x = 0.258578644 Simplifying x = 0.258578644Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.541421356, 0.258578644}
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