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Simplifying -2.5x2 + 5x = 1.9 Reorder the terms: 5x + -2.5x2 = 1.9 Solving 5x + -2.5x2 = 1.9 Solving for variable 'x'. Reorder the terms: -1.9 + 5x + -2.5x2 = 1.9 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 -1.9 + 5x + -2.5x2 = 0.0 Begin completing the square. Divide all terms by -2.5 the coefficient of the squared term: Divide each side by '-2.5'. 0.76 + -2x + x2 = 0 Move the constant term to the right: Add '-0.76' to each side of the equation. 0.76 + -2x + -0.76 + x2 = 0 + -0.76 Reorder the terms: 0.76 + -0.76 + -2x + x2 = 0 + -0.76 Combine like terms: 0.76 + -0.76 = 0.00 0.00 + -2x + x2 = 0 + -0.76 -2x + x2 = 0 + -0.76 Combine like terms: 0 + -0.76 = -0.76 -2x + x2 = -0.76 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -0.76 + 1 Reorder the terms: 1 + -2x + x2 = -0.76 + 1 Combine like terms: -0.76 + 1 = 0.24 1 + -2x + x2 = 0.24 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.24 Calculate the square root of the right side: 0.489897949 Break this problem into two subproblems by setting (x + -1) equal to 0.489897949 and -0.489897949.Subproblem 1
x + -1 = 0.489897949 Simplifying x + -1 = 0.489897949 Reorder the terms: -1 + x = 0.489897949 Solving -1 + x = 0.489897949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0.489897949 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.489897949 + 1 x = 0.489897949 + 1 Combine like terms: 0.489897949 + 1 = 1.489897949 x = 1.489897949 Simplifying x = 1.489897949Subproblem 2
x + -1 = -0.489897949 Simplifying x + -1 = -0.489897949 Reorder the terms: -1 + x = -0.489897949 Solving -1 + x = -0.489897949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -0.489897949 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.489897949 + 1 x = -0.489897949 + 1 Combine like terms: -0.489897949 + 1 = 0.510102051 x = 0.510102051 Simplifying x = 0.510102051Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.489897949, 0.510102051}
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