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Simplifying 4x2 + 0.8x + 2.16 = 9.7 Reorder the terms: 2.16 + 0.8x + 4x2 = 9.7 Solving 2.16 + 0.8x + 4x2 = 9.7 Solving for variable 'x'. Reorder the terms: 2.16 + -9.7 + 0.8x + 4x2 = 9.7 + -9.7 Combine like terms: 2.16 + -9.7 = -7.54 -7.54 + 0.8x + 4x2 = 9.7 + -9.7 Combine like terms: 9.7 + -9.7 = 0.0 -7.54 + 0.8x + 4x2 = 0.0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.885 + 0.2x + x2 = 0.0 Move the constant term to the right: Add '1.885' to each side of the equation. -1.885 + 0.2x + 1.885 + x2 = 0.0 + 1.885 Reorder the terms: -1.885 + 1.885 + 0.2x + x2 = 0.0 + 1.885 Combine like terms: -1.885 + 1.885 = 0.000 0.000 + 0.2x + x2 = 0.0 + 1.885 0.2x + x2 = 0.0 + 1.885 Combine like terms: 0.0 + 1.885 = 1.885 0.2x + x2 = 1.885 The x term is 0.2x. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2x + 0.01 + x2 = 1.885 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 1.885 + 0.01 Combine like terms: 1.885 + 0.01 = 1.895 0.01 + 0.2x + x2 = 1.895 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 1.895 Calculate the square root of the right side: 1.37658999 Break this problem into two subproblems by setting (x + 0.1) equal to 1.37658999 and -1.37658999.Subproblem 1
x + 0.1 = 1.37658999 Simplifying x + 0.1 = 1.37658999 Reorder the terms: 0.1 + x = 1.37658999 Solving 0.1 + x = 1.37658999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 1.37658999 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 1.37658999 + -0.1 x = 1.37658999 + -0.1 Combine like terms: 1.37658999 + -0.1 = 1.27658999 x = 1.27658999 Simplifying x = 1.27658999Subproblem 2
x + 0.1 = -1.37658999 Simplifying x + 0.1 = -1.37658999 Reorder the terms: 0.1 + x = -1.37658999 Solving 0.1 + x = -1.37658999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -1.37658999 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -1.37658999 + -0.1 x = -1.37658999 + -0.1 Combine like terms: -1.37658999 + -0.1 = -1.47658999 x = -1.47658999 Simplifying x = -1.47658999Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.27658999, -1.47658999}
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